Table of high Fermat-quotients for bases smaller than their associated prime

Exponential diophantine problems

Gottfried Helms - Univ Kassel (Miniatures since 07' 2007)

Table for Fermat-quotients of degree m≥2
for integer bases b<p (where p ∈ ℙ )

The following table displays p-adic-expansions of bases b, for which

bp-1 ≡ 1 (mod pm)

In ([1],2009) I discussed earlier the problem of Fermat-quotients and introduced a couple of small tools and concepts which I use here. This table focuses on data for only a specific subset of the entire problem.

The casual reader who is not aware of the concept of Fermat-quotient may look in the wikipedia (see:[wp]) first which gives some basic insight and a couple of further references/online-links.

The reader may find some quite involved related tables in the internet, see the references-section at the end of this article for some online-links to homepages which I got aware of.

Some preliminary definitions:

1) In the following I (mis)use the braces for a shorter notation to express the above statement for a more general view. (A misuse which has been helpful through all my discussions/treatizes of exponential diophantine problems.) For the case, that a number n contains the primefactor p to the m'th power I write for p's canonical exponent in n:

{n, p} = m ==> n = x ∙ pm ∙with gcd(x,p)=1

Note that this notation is a bit more algebraic/concise than "pm| n" or "n≡0 (mod pm)"because -if in the two latter two cases m is the indeterminate- then the expression gives only an upper limit and not a precise value to m. So for instance,

{2p-1-1, p} = 2

is a bit more restricted/precise than the original definition for a Wieferich-prime p which requires only

{2p-1-1, p} ≥ 2

(where we know only two solutions p=1093 and p=3511 for m ≥2 anyway).

Similary for instance

{35-1 , 11} = 2
{196-1 , 7} = 3
{7408626 – 1,7} = 7
{17590908883812 – 1,13} = 12

indicate Fermat-quotients for (3, 11), (19, 7), (740862, 7) and (175909088838, 13) of degrees 2,3,7 and 12 respectively.

2) Let's define here the term "degree of the Fermat-quotient":

{bp-1-1, p } = m ==> m is the degree of the Fermat-quotient of the pair (b,p)

3) By the p-adic-representation of the bases b which provide high Fermat-quotients for some prime p we can read the table like in the following example:

p	b	d₀	d₁	d₂	d₃	d₄	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	...
7	1	1	0	0	0	0	0	0	0	0	0	0	0	...
7	2	2	4	6	3	0	2	6	2	4	3	4	4	...
7	3	3	4	6	3	0	2	6	2	4	3	4	4	...
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...

Here the column p indicates the prime, the column b the "root" bases - "root" means here, that from b = d₀ further bases b_m can be derived according to the given p-adic digits d₀,d₁,d₂,... Actually the entry in that column is identical with the entry in column d₀ which simply contain all congruence-classes (mod p) .

The "p-adic" convention means, that the "digits" are just the digits of the number-representation of some number in the number-system to base p, so to say:

b_m = "d_m-1 ... d₂ d₁ d₀" _{base p}

so for the row with "root" base b=2 we can get the following subsequent bases b₁,b₂,...

b₁ = 2                                   = 2                         ==>        {26 -1, 7} = 1
b₂ = 2 + 4∙7                        = 30                      ==>        {306-1, 7} = 2
b₃ = 2 + 4∙7+ 6∙72            = 324                    ==>        {3246-1, 7} = 3
...
and in general
b_m = 2 + 4∙7+ ... +d_m-1∙7m-1                            ==>        {b_m6-1, 7} = m

But note, that also infinitely many bases of the form

let x a positive integer such that gcd(x,6) = 1
b₂ = 2 + 4∙7+ x∙72 = 30+x∙49 ==> {b₂6-1, 7} = 2

give also fermat-quotients of degree 2, so

{796 - 1, 7} = 2

We can conclude one more result: because we see here a set of infinitely many bases in arithmetic progression, we have even - due to Dirichlet's theorem - a proof, that for each prime p and each degree m we'll find infinitely bases b_m which are prime themselves.

So such a table essentially gives the (p-1)th roots of 1 modulo some pm in the p-adic sense and can in analogy be thought as representing the unit-roots exp(î∙π∙m/(p-1)) in the case of the complex number plane.

(end of preliminary definitions)

Note that b=d₀ being a residue (mod p) means, that all bases b gotten by p-adic-expansions beginning at a residue d₀ <>0 (mod p) are also coprime to p and have no (yet recognizable) simple restrictions, so for instance they

* can be even,
* can be odd,
and in particular
* can be prime themselves.

Sometimes tabulations of Fermat-quotients display only prime bases b - for instance because there is great relevance connected to other exponential diophantine problems like FLT -for instance by the analyses of A. Wieferich (after whom that Wieferich-primes are named) and others. But this is not intended here; here I want to display the general scheme and in that scheme I want to focus to that subset of higher Fermat-quotients where the bases are in the residue classes of the associated primes and thus smaller that that primes.

Base b smaller than prime p

The example computation in the above lines shows immediately, that the displayed bases b = b₁, simply equalling the residue-classes (mod p), are the only ones which are smaller than the prime which defines the congruence. High fermat-quotients are very rare for such cases; two prominent examples are the above mentioned two Wieferich primes p=1093 and p=3511 to base 2 where we have 21092≡1 (mod 10932) and 23510≡1 (mod 35112) or in the new notation {21092-1, 1093} = 2 and {23510-1, 3511} = 2 ; another one is p=11 and the base b=3 where we have {310 - 1, 11} = 2 .

To have such a case is equivalent to have the digit d₁=0 in the table, because that means, according to the example above

b₂ = d₀ + 0∙p1 = d₀ = b₁ ==> {b₁p-1 -1 , p} = 2

and the earliest example is that for prime p = 11 and base b₁ = 3

p	b	d₀	d₁	d₂	d₃	d₄	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁
11	3	3	0	1	2	3	6	10	8	7	0	6	3	9

(Note that in general zeros in the digits occur randomly scattered over the digits in the table)

The well known Wieferich-primes p=1093 and p=3511 are immediately recognizable in the table by this: they are the only occurences so far, where the root base (= residue d₀) equals 2 (or some small powers of 2) and the digit d₁=0. They are marked orange here:

p	b	d₀	d₁	d₂	d₃	d₄	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁
1093	2	2	0	974	227	564	478	1009	395	581	1027	834	136	534
3511	2	2	0	102	2379	495	3468	1939	2849	2386	752	3077	803	3499

Higher degrees of Fermatquotiens

For even higher Fermat-quotients we can proceed by looking for further consecutive zeros in the digits:

               b₃ = d₀ + 0∙p1+ 0∙p2         = b₀                       ==>        {b₃p-1 - 1, p} = 3
               b_m = d₀ + 0∙p1+ ...+ 0∙pm-1= b₀                      ==>        {b_mp-1 - 1, p} = m
               ...

Cases m=3

The only case of the fermat-quotient of order m=3 (where also the base is smaller than the defining prime) occurs with the prime p=113 and the base b₃ = b₁ = d₀ = 68 :

p	b	d₀	d₁	d₂	d₃	d₄	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁
113	68	68	0	0	92	4	67	65	0	13	7	106	20	16

For this I checked the primes up to p=17 389 (which is the 2 000^th prime). In the mathematical-discussionboard MSE (see[2]) one correspondent confirmed that observation and proceeded saying he had found this to be true up to p=104 729, (which is the 10 000'th prime) . In [3] we find that no further example occurs up to p ~ 3.6 ∙ 108

Cases m>3

I've not found any higher degree Fermat-quotients for pairs of bases and primes with b<p.

Gottfried Helms, 7.12.2013

Table 1, b<p:

p-adic representations for bases allowing fermat-quotients up to degree 12, where the high fermat-quotient occurs already for the "root" bases (which are smaller than the defining prime). That is equivalent to say that the p-adic-digit d₁ = 0 .

p	b	d₀	d₁	d₂	d₃	d₄	d₄	d₅	d₆	d₇	d₈	d₉	d₁₀	d₁₁
11	3	3	0	1	2	3	6	10	8	7	0	6	3	9
11	9	9	0	6	1	9	8	7	1	3	2	0	0	6
29	14	14	0	6	9	19	22	8	24	4	3	19	16	25
37	18	18	0	26	16	3	34	26	35	26	24	18	24	1
43	19	19	0	34	35	10	37	7	26	6	41	34	4	21
59	53	53	0	28	27	40	50	43	2	38	17	21	45	38
71	11	11	0	9	23	19	43	34	58	41	12	49	52	48
71	26	26	0	19	48	7	70	7	9	25	60	45	27	29
79	31	31	0	22	69	9	4	0	69	27	67	11	51	42
97	53	53	0	87	20	43	33	35	56	75	38	17	7	71
103	43	43	0	69	94	23	81	59	78	91	45	75	19	9
109	96	96	0	63	53	40	18	51	44	40	99	57	62	83
113	68	68	0	0	92	4	67	65	0	13	7	106	20	16
127	38	38	0	14	80	89	79	92	87	33	49	34	108	78
127	62	62	0	38	18	74	120	88	26	85	117	22	102	121
131	58	58	0	58	45	43	35	118	39	49	117	20	67	93
131	111	111	0	100	6	68	71	120	87	121	113	124	2	1
137	19	19	0	32	71	56	130	42	88	50	33	95	120	36
151	78	78	0	24	93	15	23	57	16	50	119	20	54	29
163	65	65	0	117	74	136	122	122	90	95	161	79	119	141
163	84	84	0	30	38	143	65	86	83	84	150	160	147	3
181	78	78	0	122	38	129	144	116	13	64	54	10	97	32
191	176	176	0	70	66	133	24	78	95	120	16	148	13	67
197	143	143	0	180	145	6	84	55	185	7	77	174	25	41
199	174	174	0	105	162	83	129	100	104	106	36	10	83	176
211	165	165	0	192	78	98	178	173	190	77	96	101	58	86
211	182	182	0	155	11	37	210	111	113	126	10	199	119	24
223	69	69	0	41	45	55	211	154	104	52	8	140	215	115
229	44	44	0	120	127	35	174	225	143	172	7	161	17	73
229	209	209	0	219	104	7	38	62	94	32	167	209	89	92
233	33	33	0	34	13	124	218	79	170	138	23	22	145	55
241	94	94	0	200	219	44	40	139	133	194	33	79	216	98
257	48	48	0	35	193	232	136	111	42	246	8	240	108	153
263	79	79	0	228	138	101	146	179	235	11	154	235	65	25
269	171	171	0	113	237	101	88	201	166	6	182	69	230	91
269	180	180	0	74	218	219	202	244	259	140	164	82	64	245
269	207	207	0	77	22	243	185	188	90	167	129	189	99	31
281	20	20	0	127	19	267	238	270	101	2	147	168	255	241
283	147	147	0	26	218	169	270	98	171	149	208	28	73	159
293	91	91	0	39	206	171	105	26	97	289	219	38	212	97
307	40	40	0	65	32	263	223	198	59	173	201	300	51	156
313	104	104	0	218	120	107	74	51	239	108	42	125	305	227
313	213	213	0	58	53	223	63	66	120	238	69	293	236	74
331	18	18	0	14	185	36	326	146	77	236	117	314	217	208
331	71	71	0	147	280	26	271	249	28	266	190	81	72	272
331	324	324	0	173	41	188	39	158	186	190	192	261	44	66
347	75	75	0	27	292	130	202	322	311	308	91	124	68	45
347	156	156	0	204	298	48	283	227	292	96	238	158	288	171
349	223	223	0	164	173	80	185	86	312	39	96	135	319	200
349	317	317	0	103	38	68	134	72	47	119	213	260	143	75
353	14	14	0	337	259	116	221	334	144	288	263	294	249	149
353	196	196	0	258	218	347	348	162	301	246	26	14	219	298
359	257	257	0	7	62	98	138	61	136	346	355	202	95	59
359	331	331	0	220	114	233	245	242	343	204	171	157	105	184
367	159	159	0	8	121	119	104	131	157	155	171	361	260	334
367	205	205	0	357	199	82	254	320	156	227	196	115	135	257
373	242	242	0	85	355	365	313	261	262	275	8	304	76	16
379	174	174	0	198	72	194	145	375	164	136	90	120	97	280
397	175	175	0	184	332	45	282	293	362	7	18	355	77	396
401	280	280	0	111	66	332	351	28	254	130	160	12	373	20
419	369	369	0	210	182	164	36	27	57	284	65	109	78	307
421	251	251	0	391	78	129	155	80	102	361	409	247	41	368
433	349	349	0	226	95	120	215	8	94	113	137	206	50	182
439	194	194	0	171	199	141	134	421	15	420	120	321	21	35
449	210	210	0	241	129	137	282	393	314	294	83	246	101	212
461	52	52	0	206	196	154	265	320	98	291	416	232	273	451
463	255	255	0	177	75	422	113	430	83	351	42	169	375	265
463	345	345	0	40	331	112	286	24	426	256	175	307	436	370
487	10	10	0	329	462	103	341	149	54	64	287	349	100	311
487	100	100	0	249	0	258	336	428	281	36	237	54	415	322
487	175	175	0	427	44	471	72	106	273	475	187	406	475	207
487	307	307	0	424	391	356	98	429	194	148	479	236	420	3
499	346	346	0	460	279	269	135	282	230	492	301	219	312	420
509	93	93	0	263	29	65	137	86	45	367	277	294	481	493
509	250	250	0	362	34	224	121	181	23	163	373	211	115	476
521	308	308	0	234	382	126	54	143	270	374	143	129	105	504
523	241	241	0	177	363	517	57	483	214	449	291	455	515	365
547	427	427	0	80	35	1	9	519	12	248	135	52	437	525
557	430	430	0	216	407	507	519	454	443	482	394	423	307	4
563	486	486	0	95	227	453	37	221	314	138	122	430	552	234
571	262	262	0	465	32	170	218	521	229	319	188	359	219	231
571	422	422	0	235	88	536	559	257	229	106	540	414	430	452
571	516	516	0	432	328	306	112	386	407	316	168	298	190	9
577	427	427	0	173	365	178	420	563	350	442	230	281	568	135
599	559	559	0	22	516	267	499	67	485	573	452	454	565	338
599	588	588	0	589	354	135	381	250	166	129	215	282	372	246
601	405	405	0	206	198	25	241	258	187	133	391	525	404	295
607	162	162	0	28	95	427	332	475	143	10	374	525	53	61
607	302	302	0	298	328	238	332	253	427	365	482	386	364	1
617	556	556	0	295	98	413	185	346	272	288	5	439	33	555
619	286	286	0	412	73	19	138	443	323	552	101	519	576	4
631	69	69	0	436	306	380	15	431	309	438	213	508	462	250
631	534	534	0	166	492	272	428	130	153	213	346	378	261	273
641	340	340	0	262	69	543	35	618	472	390	519	613	20	474
647	56	56	0	140	27	415	35	514	425	378	583	89	458	253
647	526	526	0	424	398	143	435	400	187	561	421	578	392	523
653	84	84	0	256	398	21	227	576	63	105	604	360	551	337
653	120	120	0	380	432	266	387	96	541	640	138	311	454	151
653	197	197	0	488	104	542	530	73	535	89	26	154	125	304
653	287	287	0	242	101	139	90	595	75	26	265	559	647	617
653	410	410	0	550	517	360	607	363	295	451	73	367	504	652
659	503	503	0	332	163	234	104	573	123	3	637	498	72	46
661	184	184	0	24	88	510	39	522	472	487	446	32	600	5
673	22	22	0	131	423	461	316	512	460	298	0	549	192	316
673	484	484	0	380	449	457	280	57	208	610	668	555	341	244
701	375	375	0	608	72	366	153	324	202	483	404	383	105	355
727	92	92	0	148	465	314	508	11	31	88	13	164	581	357
739	168	168	0	338	187	646	243	602	64	62	195	681	478	230
743	467	467	0	301	187	637	366	614	176	85	187	552	288	193
761	675	675	0	240	616	172	161	269	43	462	481	759	669	550
769	392	392	0	749	733	564	221	316	264	293	466	340	696	542
773	392	392	0	575	155	542	561	413	446	173	546	81	245	375
797	440	440	0	651	772	713	596	647	154	69	511	416	563	228
797	446	446	0	133	654	744	149	541	441	195	222	529	417	1
809	207	207	0	136	315	270	374	671	514	533	322	556	253	603
823	393	393	0	546	57	76	596	160	414	133	740	627	385	297
827	314	314	0	587	431	569	179	608	385	0	118	506	728	509
827	381	381	0	471	730	400	773	607	299	760	280	656	178	480
829	46	46	0	416	576	9	262	755	19	576	659	306	652	387
829	632	632	0	805	672	312	78	524	275	738	208	683	20	821
839	667	667	0	11	295	797	257	832	360	25	153	134	401	788
857	682	682	0	580	841	472	470	270	553	763	247	42	781	394
859	643	643	0	571	357	16	689	823	4	328	311	716	464	209
863	13	13	0	223	549	234	434	827	732	727	373	463	629	574
863	169	169	0	620	472	597	754	378	551	481	279	579	638	756
863	434	434	0	362	749	6	860	254	560	395	438	178	791	680
877	166	166	0	82	875	839	55	93	562	657	372	541	830	526
883	644	644	0	798	613	531	182	277	738	635	393	228	723	250
883	657	657	0	539	735	114	572	515	757	846	839	13	214	216
883	754	754	0	765	92	747	821	54	410	403	875	655	14	828
887	292	292	0	455	170	748	775	370	490	186	715	498	157	698
907	127	127	0	137	271	198	33	837	240	191	571	828	476	309
907	761	761	0	455	797	276	341	797	449	578	290	269	406	425
907	771	771	0	409	815	892	441	213	535	209	336	728	505	730
911	328	328	0	672	30	58	222	866	865	17	817	391	875	619
919	457	457	0	855	700	794	688	724	363	145	798	323	119	552
941	292	292	0	172	395	299	939	178	489	440	7	689	635	512
947	208	208	0	312	35	913	584	565	6	410	775	879	299	809
953	325	325	0	572	927	616	271	312	900	736	196	723	30	312
967	287	287	0	825	375	427	750	261	32	728	516	219	280	682
971	296	296	0	948	665	509	708	761	603	285	562	329	661	4
977	238	238	0	347	362	124	792	240	200	756	161	243	741	462
977	354	354	0	850	276	686	637	400	930	929	95	105	884	144
983	419	419	0	213	574	546	313	131	413	53	233	388	969	833
991	976	976	0	575	10	287	151	223	170	673	938	644	102	782
997	252	252	0	263	89	35	122	232	177	340	31	656	430	975
1009	990	990	0	124	622	369	650	10	652	877	737	519	691	289
1013	899	899	0	53	939	233	19	435	933	764	290	801	955	370
1019	705	705	0	567	21	532	557	518	854	25	529	594	417	158
1021	551	551	0	260	41	772	221	55	674	42	959	304	485	635
1021	637	637	0	589	121	633	88	773	342	354	91	804	655	333
1031	158	158	0	480	830	356	934	477	622	710	463	770	100	369
1051	806	806	0	473	472	90	578	635	631	429	987	224	39	242
1061	508	508	0	688	141	676	860	1001	444	150	103	850	825	635
1061	917	917	0	927	579	89	823	291	615	182	526	837	78	720
1069	487	487	0	200	281	102	91	1020	732	285	585	688	933	294
1087	617	617	0	69	32	215	116	253	343	137	787	598	20	1069
1087	740	740	0	667	801	656	635	137	1075	554	970	612	603	320
1091	691	691	0	344	654	419	729	142	357	405	134	588	560	604
1093	2	2	0	974	227	564	478	1009	395	581	1027	834	136	534
1093	4	4	0	617	911	22	127	436	652	1082	282	490	680	617
1093	8	8	0	758	548	1017	484	587	858	153	261	275	1033	699
1093	16	16	0	564	734	507	841	302	601	527	806	750	801	954
1093	32	32	0	317	743	855	245	337	933	967	356	787	38	234
1093	64	64	0	105	35	624	721	693	233	641	256	810	308	709
1093	128	128	0	245	446	816	460	1024	275	545	532	401	285	940
1093	256	256	0	560	551	976	443	773	450	275	240	1071	524	75
1093	512	512	0	167	421	1054	720	588	456	112	1072	227	128	1009
1093	1024	1024	0	614	571	46	499	179	113	286	721	989	468	139
1097	425	425	0	26	245	1049	249	341	724	106	41	347	69	1011
1097	579	579	0	763	103	818	258	393	810	261	805	264	120	973
1097	776	776	0	620	916	30	815	652	151	357	698	307	129	138
1103	284	284	0	835	17	453	446	84	354	412	589	730	1074	886
1103	793	793	0	580	1071	306	463	830	699	859	172	222	268	395
1103	1054	1054	0	344	685	433	201	756	483	5	245	675	558	634
1109	76	76	0	939	809	237	480	479	1107	637	129	392	867	156
1109	1082	1082	0	783	361	697	958	48	616	149	794	60	133	1028
1117	1066	1066	0	898	390	571	219	1096	267	878	759	80	868	135
1123	897	897	0	639	1027	895	574	845	571	509	433	73	773	113
1123	1012	1012	0	371	669	175	423	392	604	1042	815	547	645	614
1163	78	78	0	1098	801	411	910	227	499	290	721	643	885	799
1163	170	170	0	428	1101	877	826	57	692	90	574	687	744	605
1163	241	241	0	364	519	987	983	184	662	156	159	92	997	997
1163	618	618	0	941	548	1152	1052	932	236	827	244	465	173	961
1181	874	874	0	304	948	177	215	662	90	55	13	207	287	575
1187	184	184	0	350	618	719	797	67	157	998	345	1017	536	1036
1187	315	315	0	503	1000	945	140	370	541	378	988	948	1132	40
1193	622	622	0	941	639	206	110	543	439	449	389	884	88	140
1201	206	206	0	411	1159	1118	848	842	465	457	1129	292	91	517
1213	178	178	0	20	837	172	364	671	1058	94	1145	1170	110	1039
1217	1188	1188	0	126	385	746	59	346	177	424	356	890	72	454
1223	997	997	0	743	770	969	557	48	55	398	223	771	332	183
1229	821	821	0	1021	765	663	1085	785	661	1217	812	285	612	354
1249	326	326	0	385	232	1234	1185	1083	219	1074	176	99	406	24
1279	683	683	0	170	53	846	1261	481	971	418	535	375	587	287
1283	45	45	0	791	1182	60	228	365	911	1265	1000	455	251	524
1291	62	62	0	17	698	644	798	311	167	837	823	866	1160	319
1291	1148	1148	0	143	119	24	605	147	961	971	1103	732	503	1076
1291	1286	1286	0	1166	961	41	104	765	57	690	797	190	757	476
1297	156	156	0	200	204	688	901	932	41	624	1128	67	85	477
1303	528	528	0	383	754	864	147	1292	651	1285	338	1055	152	1249
1321	403	403	0	899	701	737	674	388	440	885	1064	1095	252	1307
1327	585	585	0	968	642	607	640	378	1080	438	1073	247	1241	448
1327	1149	1149	0	707	865	1142	291	1174	216	1326	266	54	448	133
1361	228	228	0	1135	1151	901	1336	386	44	558	1234	923	1313	838
1367	411	411	0	821	461	915	1129	35	538	716	634	223	1124	1358
1373	884	884	0	291	855	67	378	133	350	331	244	979	1343	1014
1381	429	429	0	250	1342	1333	1196	842	241	273	1002	71	659	223
1381	653	653	0	1157	633	198	1002	1069	345	416	171	120	1354	990
1399	328	328	0	234	1124	836	567	1292	70	462	1223	28	412	264
1399	987	987	0	1081	1095	1373	1158	944	999	786	764	1083	941	1130
1409	1164	1164	0	191	900	260	426	1401	1126	1215	748	1271	31	1220
1429	688	688	0	965	39	739	1081	280	995	462	636	820	913	1174
1429	1401	1401	0	1261	620	1297	515	194	1253	144	945	639	703	502
1439	319	319	0	180	1292	1262	213	1217	1281	930	1111	698	69	362
1447	584	584	0	784	664	929	1198	1312	882	256	972	75	137	341
1453	365	365	0	1325	1105	1307	1371	702	255	1159	856	945	424	960
1453	378	378	0	1242	1441	129	59	662	946	1278	1063	801	1452	117
1459	1082	1082	0	544	379	742	1112	1340	292	1061	1180	1124	698	876
1471	1195	1195	0	1397	299	935	820	319	95	1171	855	395	152	920
1483	421	421	0	1302	215	604	640	1343	1203	990	1062	138	975	162
1483	1061	1061	0	264	408	907	1421	487	226	897	1365	1434	749	1481
1489	1211	1211	0	556	88	270	1432	1470	412	126	518	949	6	582
1493	164	164	0	704	518	340	810	833	1474	846	704	592	817	152
1493	488	488	0	1016	1446	1266	958	950	854	799	1103	245	633	690
1499	941	941	0	981	1381	1464	692	260	963	1104	557	22	1084	634
1499	1172	1172	0	1375	855	1059	635	118	1181	1408	469	1232	1096	1
1511	934	934	0	953	1124	161	281	787	1217	569	997	23	524	976
1523	1032	1032	0	1478	524	1315	132	326	23	62	1499	1183	1429	309
1523	1246	1246	0	646	83	120	916	960	240	680	604	78	111	1322
1531	472	472	0	574	1110	1386	467	1395	180	765	1143	1155	164	1241
1531	1238	1238	0	1323	1331	401	904	724	1315	853	926	280	731	835
1549	855	855	0	1003	313	1545	254	1010	256	1073	197	1028	586	448
1549	1069	1069	0	1248	215	543	885	1211	194	1459	585	265	1319	444
1553	392	392	0	588	1267	615	1068	1300	144	1149	1018	230	347	52
1553	568	568	0	321	774	1018	641	1413	1423	1035	1369	225	199	875
1559	1454	1454	0	56	668	1379	798	1209	98	538	701	963	826	19
1571	1265	1265	0	116	859	989	111	649	1	538	780	6	1080	201
1579	603	603	0	709	1177	1270	1286	1092	1305	592	55	1000	1327	1496
1579	906	906	0	201	345	1225	73	749	532	134	1381	1115	754	24
1579	1235	1235	0	619	916	1548	1353	1051	681	1411	487	199	1283	289
1597	453	453	0	473	345	564	567	998	205	1548	1152	1016	148	499
1601	1420	1420	0	1	1562	600	336	214	1199	81	638	1296	384	139
1607	874	874	0	669	1209	508	82	402	146	1188	450	643	441	92
1607	1253	1253	0	64	1021	489	1135	786	892	1418	1564	1437	326	1497
1613	35	35	0	359	1194	748	952	514	222	858	510	851	401	1067
1613	1225	1225	0	935	1332	636	1408	745	906	434	185	333	645	329
1619	371	371	0	37	1339	439	801	1251	1424	19	782	729	1067	226
1619	536	536	0	22	116	95	1380	1340	394	1364	1198	1129	710	24
1621	558	558	0	256	278	405	1138	1452	564	925	313	1599	732	636
1621	746	746	0	1560	1116	604	652	1436	1356	39	1370	1253	486	1301
1627	923	923	0	400	1481	342	1080	1053	842	1070	1303	1240	146	1598
1657	427	427	0	1511	620	1647	1265	1649	510	96	739	1301	333	648
1657	1481	1481	0	1616	369	1222	183	464	566	254	292	475	739	177
1663	709	709	0	1426	1234	998	320	1239	271	173	352	16	68	1158
1667	463	463	0	59	1534	373	1039	315	1371	261	968	884	1362	295
1669	221	221	0	549	1627	596	1093	1511	28	1326	1174	1071	1611	63
1669	423	423	0	964	1352	892	9	319	1495	1211	1539	1127	83	31
1697	461	461	0	1524	1309	952	584	1328	599	1067	56	178	1569	135
1697	857	857	0	936	853	359	1379	883	944	1072	800	603	1148	758
1697	1392	1392	0	1166	1436	204	698	472	584	1306	283	1038	1354	1648
1741	119	119	0	1495	923	1249	626	163	383	1661	1136	1128	1715	1022
1741	278	278	0	381	1252	1508	274	976	1169	138	792	1627	388	1522
1741	1234	1234	0	459	551	150	1064	1352	498	18	1049	136	714	605
1747	982	982	0	1063	1005	724	1201	841	1180	1126	740	451	173	493
1747	1153	1153	0	765	1473	1650	380	1547	226	1292	171	887	37	1323
1777	1381	1381	0	696	1454	1418	1178	1639	694	845	406	1684	807	267
1783	1139	1139	0	1196	1068	121	899	478	411	763	194	1354	1629	216
1787	631	631	0	254	1656	533	1086	1108	799	820	1471	1583	233	1397
1789	449	449	0	1708	185	555	787	1776	835	1406	699	180	1258	987
1801	1791	1791	0	113	1777	482	988	289	1072	111	1202	1483	593	246
1831	434	434	0	1743	10	1015	263	439	241	1571	1771	636	755	215
1847	189	189	0	2	845	900	578	1589	578	538	1146	1276	40	1553
1867	828	828	0	1538	1360	537	1013	1041	1402	1341	1465	1335	1854	17
1873	731	731	0	1008	1732	448	711	1151	663	1416	740	1715	1564	1246
1877	213	213	0	49	341	1503	1659	1184	439	335	1028	118	146	1216
1877	1091	1091	0	1050	475	1570	1623	1478	1350	203	1421	1214	865	27
1889	583	583	0	223	72	1232	1684	1711	191	555	1418	1435	414	1493
1933	963	963	0	319	1535	1106	1366	281	316	432	68	683	221	1594
1933	1691	1691	0	1890	818	1519	855	1798	1628	1111	1835	952	1073	280
1949	54	54	0	291	254	1666	420	857	941	842	950	1722	1424	255
1949	704	704	0	1097	786	1844	3	1176	1532	510	460	1883	783	1748
1973	803	803	0	1212	1764	1754	894	823	87	1775	1596	1242	1773	1456
1987	1862	1862	0	757	873	1734	495	624	183	1668	680	605	222	1845
1993	277	277	0	267	1846	401	559	477	258	776	4	1085	895	1005
1993	1747	1747	0	691	29	1637	975	825	507	961	703	1083	1879	56
1997	866	866	0	1987	1832	149	646	1233	1881	107	326	804	1549	1802
1999	87	87	0	418	187	1906	1663	726	1585	337	1655	1176	230	1662
1999	143	143	0	552	684	1593	976	954	1463	1490	428	1154	1218	1364
2011	1993	1993	0	1511	1387	1883	1374	309	206	131	1994	268	818	1745
2017	1563	1563	0	1168	1543	1583	354	1492	502	1689	1758	722	1630	181
2029	1715	1715	0	1276	1473	939	615	483	1579	210	204	452	1331	98
2063	1376	1376	0	1397	1777	898	1354	950	1362	1440	697	496	1521	1160
2069	1470	1470	0	96	25	1997	963	94	1536	244	207	680	496	660
2083	1705	1705	0	1410	370	801	567	1973	1383	608	1486	1232	1404	1457
2087	206	206	0	1543	1815	1194	175	1467	576	481	751	961	1876	1782
2089	515	515	0	328	1985	1488	661	1353	1420	936	1118	1382	788	1051
2099	1027	1027	0	2081	25	1921	1447	350	1536	1055	457	748	1829	1066
2113	652	652	0	1938	650	1069	1174	1247	920	103	422	1260	329	853
2113	957	957	0	748	1512	216	1076	1957	608	1732	1186	824	2053	1494
2137	95	95	0	2008	1924	1857	966	2005	249	2136	1984	1629	1994	383
2141	452	452	0	913	483	724	1890	1876	1628	248	458	70	12	1166
2141	474	474	0	189	1105	1217	417	1484	1077	815	525	370	1578	702
2143	1465	1465	0	677	1860	1647	1785	701	9	1304	921	2059	89	1538
2153	981	981	0	1845	1876	1426	1950	1718	591	1321	1586	210	1274	1620
2161	865	865	0	555	59	479	1576	1322	1060	2142	1988	558	1442	1489
2161	1576	1576	0	1752	854	1081	219	550	987	1803	841	860	1312	57
2179	831	831	0	108	52	1853	692	2021	531	1282	683	1332	1867	444
2179	1640	1640	0	632	994	1886	1549	630	1756	424	494	458	791	1715
2179	2123	2123	0	1954	1956	2030	1597	1276	1014	1483	675	810	841	1077
2203	184	184	0	2029	1575	1503	2127	1502	1058	490	1496	1035	146	1679
2203	209	209	0	2121	808	204	1194	1262	215	904	176	2133	922	518
2203	767	767	0	860	252	481	2185	781	52	894	1280	167	1122	309
2203	2037	2037	0	451	656	1247	2018	1533	1791	478	972	417	474	1522
2213	367	367	0	1228	1160	574	1153	650	1688	2029	1172	1283	328	1598
2213	574	574	0	410	539	1365	256	1027	1418	2018	1606	1061	1196	687
2213	832	832	0	1208	995	360	748	1692	1737	1047	2139	1615	1286	1681
2221	659	659	0	1451	1708	515	595	451	1211	996	645	734	1157	523
2221	1128	1128	0	23	927	1779	40	1689	1878	2084	352	1179	2213	1284
2221	1404	1404	0	640	626	1987	395	1712	657	142	1162	456	1113	207
2243	1372	1372	0	1361	794	477	1623	1244	1301	227	335	118	1831	875
2251	151	151	0	125	1282	2185	1864	1858	30	1129	1955	2141	860	893
2251	1935	1935	0	124	1519	857	12	1232	1439	568	1766	363	1812	814
2267	538	538	0	1901	129	83	502	1099	1371	908	950	1738	1274	1670
2267	1508	1508	0	262	408	108	974	150	1913	2087	185	1218	1827	2250
2269	254	254	0	532	1306	515	1608	2248	770	1826	66	1567	469	486
2273	1797	1797	0	2080	58	1079	497	500	2104	1152	236	117	463	586
2281	1100	1100	0	378	1922	1948	2187	2144	849	1052	1312	2245	138	1284
2281	1657	1657	0	2226	2185	1331	556	1963	1985	1889	1038	1036	40	682
2281	1975	1975	0	2272	715	452	965	2240	1672	1514	770	807	106	1665
2297	1426	1426	0	456	149	2106	728	526	1474	381	1807	1426	1429	971
2297	1696	1696	0	2265	1121	1440	2143	1262	833	1445	1615	42	28	454
2309	823	823	0	788	2220	146	1746	1400	94	1353	1760	2245	148	1149
2309	1453	1453	0	2010	364	331	1686	421	1238	1735	1635	652	2115	2062
2309	2222	2222	0	626	452	670	391	717	1798	602	1049	245	406	499
2311	473	473	0	1283	1620	338	1274	793	198	2087	1993	1079	394	1716
2311	2024	2024	0	1532	1380	1619	1505	219	1490	2284	829	666	2148	2110
2311	2170	2170	0	1489	1888	128	1543	1253	1125	1956	1625	1334	10	442
2339	892	892	0	2120	1969	661	595	955	115	1366	2259	2245	1118	780
2341	2074	2074	0	553	1547	1920	2269	519	1260	1830	1656	1260	1278	239
2351	1037	1037	0	1909	1300	246	204	1509	1875	1719	2304	397	950	1132
2351	2078	2078	0	390	2033	224	687	861	427	1819	2282	55	2136	2341
2357	1853	1853	0	1300	2011	1924	710	2321	1293	992	316	1831	761	1809
2371	1493	1493	0	155	1036	1045	1558	1205	2138	1197	2100	1713	1054	2235
2371	2313	2313	0	1910	2112	1246	394	1383	1536	1297	854	2040	1153	1451
2377	507	507	0	1831	265	1214	714	459	877	374	878	122	1576	686
2389	1696	1696	0	2073	1062	1104	53	897	632	797	64	1340	2085	1435
2393	431	431	0	408	1532	713	37	1886	855	454	901	106	2093	948
2411	1016	1016	0	1887	989	1188	1018	2126	1472	757	1865	635	993	1290
2447	923	923	0	543	856	447	277	2173	190	869	1812	933	259	1782
2459	982	982	0	270	422	763	95	1116	2268	1101	1868	933	73	1494
2467	1463	1463	0	1190	913	2077	24	1717	1513	1255	3	245	705	715
2473	429	429	0	923	779	429	1320	1638	1711	1968	47	526	777	489
2473	1787	1787	0	1760	1573	1201	1174	210	1560	2045	2434	510	1533	1596
2477	779	779	0	156	205	1414	1637	559	1766	225	2370	228	2371	378
2477	1169	1169	0	507	348	840	1694	1449	128	333	170	1870	1092	1676
2503	1449	1449	0	2142	637	1136	2086	713	2006	2303	249	1739	778	1088
2503	2434	2434	0	805	2082	2295	1674	1857	420	2285	1568	1931	1320	2411
2549	915	915	0	1614	379	148	1260	2262	1466	1332	2025	1148	1014	1091
2551	756	756	0	540	1467	192	2325	1230	2144	192	886	642	2271	1541
2551	1820	1820	0	2018	1770	2240	941	2246	901	2079	861	567	2325	57
2551	2032	2032	0	385	1447	874	2163	2295	2195	2122	241	2283	1403	906
2593	2561	2561	0	1620	746	358	1414	1389	1211	1949	16	1839	2066	1181
2609	2200	2200	0	515	560	1937	284	665	1558	205	532	1078	347	1855
2621	2062	2062	0	752	326	22	2501	651	114	2133	1446	911	754	1272
2659	445	445	0	2575	569	779	2173	1095	2422	2611	81	709	2384	2203
2659	2103	2103	0	2050	6	29	300	2150	72	2041	1243	464	511	635
2671	560	560	0	2643	2124	543	2512	12	2339	1991	377	688	1824	224
2671	2063	2063	0	228	348	1461	773	453	2037	1774	960	2164	1509	1637
2671	2271	2271	0	2066	1894	64	383	261	420	1884	1047	2575	908	777
2677	680	680	0	468	2141	742	1719	2170	276	258	762	1866	2401	2115
2677	2544	2544	0	1439	29	1651	812	504	2212	2378	165	1557	2001	2274
2677	2653	2653	0	1690	2342	698	1853	2180	117	889	711	1658	1096	101
2683	2571	2571	0	447	983	1234	401	692	493	1165	1031	1266	2299	1493
2687	372	372	0	503	2160	1584	2537	723	2114	1821	1283	470	1713	1608
2687	446	446	0	1760	1600	2048	368	574	687	2038	1939	199	2510	474
2689	2446	2446	0	65	1742	134	1316	414	1440	686	1123	1893	2223	164
2693	12	12	0	1	515	2219	1677	654	320	670	795	961	1851	333
2693	144	144	0	24	1588	2094	902	2609	2273	1643	96	1785	156	2319
2693	1728	1728	0	432	1654	18	2474	2342	1615	1103	1438	1132	56	855
2707	1182	1182	0	2106	2700	2180	25	7	1568	30	1448	526	2190	253
2707	1347	1347	0	883	1138	904	813	898	18	317	215	997	1960	1657
2707	2338	2338	0	501	806	1008	642	283	525	630	1947	1757	2263	572
2719	1487	1487	0	2527	1914	2535	573	859	630	1680	186	563	1137	728
2719	2269	2269	0	302	1065	498	1563	54	1998	1316	971	1470	1631	1103
2729	744	744	0	1631	472	40	1753	2543	256	2687	836	2011	1025	673
2731	1534	1534	0	1637	477	94	2512	701	514	2643	1975	2669	1136	2718
2731	1577	1577	0	863	2081	2113	1964	519	2712	2126	2458	523	57	917
2731	1872	1872	0	1620	2452	396	2623	256	16	1333	97	530	900	2573
2731	2290	2290	0	2279	2037	499	2117	1362	285	1444	705	2104	1087	365
2741	68	68	0	1041	975	1600	1847	588	1217	551	1375	1241	851	2034
2753	445	445	0	1684	2244	284	1426	2363	2068	900	1733	1367	2001	102
2777	59	59	0	236	217	187	1895	1014	2755	446	1475	1060	870	869
2789	1888	1888	0	1033	1136	189	2531	1679	1203	914	2442	1194	2707	488
2789	2479	2479	0	1251	1479	1106	2490	274	43	1281	798	1138	2554	816
2789	2520	2520	0	915	1775	255	2407	2747	2230	724	1191	523	1062	2365
2791	122	122	0	1704	693	888	1341	1531	1498	2757	27	1557	778	402
2791	2389	2389	0	164	1578	1432	2763	1513	1786	1470	2456	772	998	856
2791	2565	2565	0	1042	2556	962	1071	2269	1734	1350	1857	18	2634	1776
2797	2465	2465	0	841	503	773	187	2696	1417	611	376	2534	2775	1152
2801	1341	1341	0	381	2189	1432	2328	2180	2067	1430	2649	1599	1482	1883
2803	2131	2131	0	846	1378	1757	542	1260	1950	2414	732	1962	1341	977
2833	479	479	0	2823	2636	2285	535	862	2067	2234	358	1437	1283	429
2833	1516	1516	0	915	615	2600	2570	1431	98	301	2453	1080	1875	902
2837	940	940	0	2039	2289	622	698	2063	320	1910	2537	207	1355	150
2837	1404	1404	0	1512	1249	1942	2025	2293	996	1090	2309	286	1840	452
2843	2465	2465	0	1069	250	274	939	2286	317	2434	584	1711	2329	88
2851	932	932	0	148	1750	1738	2497	1494	1166	2037	1500	838	1228	92
2861	1907	1907	0	1976	1454	1475	2695	271	729	2643	2167	2609	1872	196
2879	975	975	0	1845	558	2469	2113	877	507	2348	1101	1779	612	1151
2887	1731	1731	0	2459	192	218	1916	849	394	1500	598	1667	1407	2846
2897	2201	2201	0	1961	2050	433	74	218	1547	44	853	2194	1804	1260
2903	1636	1636	0	2201	266	1371	549	2484	2214	427	1116	1493	401	2693
2909	1394	1394	0	194	1632	2385	656	2180	249	946	432	2554	819	1309
2927	1980	1980	0	2693	806	728	2034	25	629	1524	1182	2797	2180	1201
2939	1706	1706	0	2351	194	1591	2791	2143	985	627	2638	1877	40	518
2953	2487	2487	0	1774	1043	1138	2498	1929	515	1271	1630	2425	2545	1797
2963	672	672	0	823	124	2510	801	1003	2837	2605	1258	1687	1061	1607
2969	1118	1118	0	609	1873	1202	2093	1637	691	2048	1906	528	1721	1839
2999	2065	2065	0	1611	1683	2504	2547	2106	1550	2912	1934	435	349	2233
2999	2253	2253	0	399	1658	607	2492	387	2215	1126	2300	1989	1774	936
3001	700	700	0	2861	958	1177	2066	443	158	790	372	2281	1598	2401
3019	1267	1267	0	2993	3012	2831	2788	1064	1968	1447	1941	2408	21	909
3023	2544	2544	0	2954	1980	499	292	975	1627	2774	1442	827	1702	2238
3037	79	79	0	777	307	18	779	751	1642	1810	2465	2758	1101	2236
3037	424	424	0	1342	145	503	534	115	2419	2938	1735	2873	2510	1046
3041	1358	1358	0	1704	2155	764	2952	516	1685	2639	2947	1188	148	1548
3041	2149	2149	0	662	2602	2098	2563	432	2857	1978	2449	2873	1569	2548
3079	173	173	0	2048	1017	926	649	2247	1445	985	1329	2158	2313	2916
3083	1119	1119	0	1694	2677	1634	1106	2948	1070	1581	1565	2539	1831	2970
3109	2107	2107	0	2732	2734	2782	2559	2474	510	1539	2602	2520	2096	343
3109	2962	2962	0	2395	2457	1065	3106	2253	2673	2769	35	2327	1312	504
3119	1083	1083	0	2495	2465	2081	1531	1437	1524	1671	3026	453	1496	596
3121	2322	2322	0	1365	1947	2188	2460	2668	541	720	3016	2542	3037	1593
3121	2873	2873	0	858	11	3078	2463	1697	2237	1286	1909	138	492	1370
3163	1151	1151	0	1077	1801	2285	619	679	2006	256	2172	3159	971	2939
3167	1972	1972	0	1175	967	1596	1496	2419	2047	89	800	2995	254	266
3181	2813	2813	0	200	2916	1819	823	2805	1871	2604	66	407	1601	1900
3191	738	738	0	2967	2968	1455	1051	1885	199	2209	127	3101	1220	1737
3191	1916	1916	0	824	2998	2251	2013	2955	969	2552	51	3050	1475	2346
3191	2464	2464	0	804	401	1794	640	511	436	936	1139	2493	2650	508
3209	1833	1833	0	534	1083	1606	1822	485	3167	308	1921	2895	1802	1648
3209	3107	3107	0	3159	222	2107	694	371	1864	2702	2793	983	2735	2825
3217	1748	1748	0	3120	1153	3126	779	1985	2760	1706	2068	1078	1761	478
3251	1831	1831	0	1509	753	882	2992	2820	1086	1190	1630	1489	2623	2462
3253	638	638	0	15	2532	2014	1042	3169	1564	391	1034	1615	1769	1103
3253	2217	2217	0	1924	2118	452	1826	2022	915	2598	1156	2281	692	2725
3253	2807	2807	0	2774	2480	1256	2259	2909	2564	715	463	1713	2722	1130
3257	419	419	0	2649	2535	519	295	508	1415	2476	2112	802	1260	138
3259	1884	1884	0	1139	1561	735	419	2188	2043	1209	921	1785	2299	109
3259	1977	1977	0	650	2911	406	3021	410	855	2849	1463	2663	2217	559
3271	1927	1927	0	388	3170	1015	1122	607	270	2637	2583	588	1070	2237
3301	2352	2352	0	773	1702	1166	3217	294	262	1657	231	1283	381	490
3307	322	322	0	2954	2928	271	1219	190	2674	1191	968	198	2808	1573
3313	1617	1617	0	3120	3302	1781	1798	2608	3255	1393	2954	2076	481	2839
3313	2306	2306	0	627	3295	788	3059	1423	1961	404	863	1182	2551	515
3331	3147	3147	0	2610	3185	1025	2240	1710	2461	2147	2482	1576	2532	1527
3343	2631	2631	0	1905	2489	2366	2148	2846	2527	264	125	2156	162	27
3359	2768	2768	0	2888	1748	122	697	281	2606	209	2927	49	2950	1336
3371	2734	2734	0	3075	1366	3157	2553	333	1253	2806	227	927	981	1170
3373	527	527	0	282	2806	2343	1323	528	620	3004	345	2774	2525	2102
3373	1238	1238	0	3346	1505	897	523	3349	1392	3282	2708	1717	1811	859
3373	1686	1686	0	1578	1798	2732	232	175	202	1907	1746	551	106	1744
3373	2739	2739	0	516	1412	2886	2617	1802	2495	729	1000	3141	326	2253
3389	1404	1404	0	1839	2783	1614	1421	2434	3090	1180	644	2500	1990	2561
3389	2589	2589	0	862	6	2500	2228	3232	1216	323	650	685	2406	809
3413	1332	1332	0	1930	585	2863	2813	3387	1125	1489	582	1641	3010	473
3433	1056	1056	0	3286	1300	2517	526	3150	1088	1408	1971	1329	726	2197
3433	1356	1356	0	2833	406	762	2015	559	1889	3327	2290	358	2742	1302
3457	2602	2602	0	3084	3368	2277	2551	2083	2035	2825	256	3242	2350	2236
3457	3043	3043	0	1217	3260	1247	1405	2038	1261	450	298	1702	78	1616
3463	1193	1193	0	562	1953	2163	1554	633	784	942	1821	3388	2130	2198
3463	3438	3438	0	1228	1066	3030	1927	2304	3161	2518	417	1882	3082	2631
3469	786	786	0	3455	2014	514	838	2159	1262	298	282	2041	3412	1390
3491	2150	2150	0	1531	2094	1853	425	1684	1381	1125	2180	3090	1611	505
3491	2620	2620	0	2825	735	2665	660	208	2003	469	1864	2262	2893	2433
3511	2	2	0	102	2379	495	3468	1939	2849	2386	752	3077	803	3499
3511	4	4	0	408	2494	1853	629	3457	84	510	1168	1265	544	3334
3511	8	8	0	1224	460	1663	780	1860	936	860	2698	2506	2669	2204
3511	16	16	0	3264	2397	2232	296	1011	1841	3396	576	109	2459	3039
3511	32	32	0	1138	728	1246	961	901	2045	384	1297	3209	2684	3145
3511	64	64	0	2029	343	1012	1430	1200	780	470	2968	435	1984	1073
3511	128	128	0	53	1972	1957	2929	1096	1093	1391	3470	1288	2042	1512
3511	256	256	0	2629	3002	2547	1082	3161	1428	2870	246	2696	1432	1807
3511	512	512	0	3282	611	3404	338	1893	2015	816	1753	3309	2421	3198
3511	1024	1024	0	2612	969	2000	1944	808	820	409	1573	2460	838	1820
3511	2048	2048	0	831	1431	2067	2217	2514	464	2985	377	3291	2533	1808
3541	1146	1146	0	1765	493	369	2997	2147	3005	3181	495	942	3259	2955
3547	2331	2331	0	3130	790	343	2868	991	1468	2050	1616	1041	1666	851
3557	3138	3138	0	144	3037	2770	2876	973	668	36	884	3393	2723	2911
3557	3319	3319	0	1566	37	1434	3088	673	1024	1896	451	1058	1429	1079
3571	35	35	0	1529	1258	2172	524	3010	3540	853	807	3410	3188	2937
3571	598	598	0	1097	995	2116	2570	177	514	1769	2059	1401	2185	3497
3571	1225	1225	0	3471	2385	918	2664	1625	327	572	2285	1935	619	2849
3581	220	220	0	1730	1487	1325	2589	757	1377	1551	333	1034	324	774
3583	755	755	0	473	365	1972	568	3097	19	406	637	521	3218	1628
3593	1171	1171	0	3045	559	1808	1851	2246	2589	3367	2762	2370	3431	1769
3607	1418	1418	0	3538	3090	1240	798	3559	350	739	2206	2415	339	1778
3607	2724	2724	0	2589	2904	2068	3535	1258	734	10	1966	537	1071	2893
3613	252	252	0	3385	148	1204	3182	2497	3274	1249	3442	3376	3060	169
3613	1848	1848	0	2965	2967	3389	788	622	1259	787	2793	1591	110	41
3617	310	310	0	2194	987	895	2217	330	1015	338	3610	2121	3148	2629
3617	1459	1459	0	243	2707	2983	3598	880	668	683	3385	2647	3248	1851
3617	3371	3371	0	1791	3490	2990	1930	803	3357	1542	3122	2245	3543	2847
3623	1774	1774	0	3490	3343	1295	3246	2137	2120	1765	1985	2961	738	1278
3631	2493	2493	0	2031	2320	3468	1729	1666	2205	177	2068	2995	3143	986
3631	3619	3619	0	342	2427	3011	2041	2226	623	874	2743	646	716	168
3659	404	404	0	2689	1361	997	1144	2922	1595	2131	1953	2523	67	1265
3671	1523	1523	0	1155	3345	2284	1546	2232	1539	1996	801	3524	2082	3174
3671	2558	2558	0	619	2297	3019	296	364	2336	705	168	801	3408	2491
3673	3666	3666	0	2324	1133	3193	2967	393	2829	3480	987	1860	1720	1102
3677	1473	1473	0	184	1788	2809	765	2230	2542	2143	2404	986	1771	1157
3677	1657	1657	0	2151	531	1687	207	1854	3127	3491	136	2064	1551	954
3691	2717	2717	0	1117	3665	1345	2618	465	2730	1822	2876	535	2810	756
3709	1749	1749	0	2552	2314	3108	3296	2984	1875	587	1745	1111	2758	2674
3719	3060	3060	0	498	1343	1857	1946	3396	855	1796	3270	2945	1845	2607
3727	3309	3309	0	381	1870	1579	1706	15	1205	1962	1286	1318	1832	1712
3739	2383	2383	0	404	1767	106	3411	1019	1795	2671	2626	3269	2492	3717
3739	2476	2476	0	3608	1958	1748	331	2534	980	2955	550	3643	471	555
3761	108	108	0	288	2234	1014	1673	2689	2195	1195	2049	129	3071	2602
3767	1209	1209	0	2273	3091	3587	1572	2856	222	3709	1111	1957	1812	2776
3767	2405	2405	0	282	3	796	2337	2942	1417	3639	572	3009	1398	1697
3779	3179	3179	0	3052	725	1778	2674	258	466	2350	953	343	308	2947
3793	1410	1410	0	2505	1314	2368	537	2683	2579	262	1621	1735	1306	2321
3797	1867	1867	0	2225	856	3631	2523	3276	1477	2439	1366	2847	3512	2690
3803	1909	1909	0	1871	1305	3094	88	1692	779	2257	2911	654	2281	661
3821	1944	1944	0	2511	381	1780	752	1809	1545	789	3455	129	2533	909
3833	272	272	0	2421	1899	941	14	2559	3552	2512	1884	2627	255	2883
3833	1193	1193	0	1353	505	150	2395	1831	2983	3527	1096	1079	3620	1026
3847	705	705	0	2676	559	3025	459	1815	3652	2810	2448	3774	1378	510
3847	1561	1561	0	3567	2193	3373	1034	2347	1599	928	1927	1392	2198	385
3851	2919	2919	0	1468	2545	3173	3789	3731	3485	2185	3274	1689	3695	3850
3853	2014	2014	0	3467	341	3767	2236	1697	3551	257	729	1144	2532	1088
3853	3846	3846	0	1253	3515	1449	1787	1805	444	2950	558	1529	3520	1202
3863	3735	3735	0	266	2603	2791	1728	3133	467	1231	748	2242	3438	2913
3877	901	901	0	2480	434	42	1624	2123	2933	376	111	1529	1984	1584
3877	1698	1698	0	3793	2031	1842	2932	1630	206	2106	891	437	2813	1690
3877	1968	1968	0	1687	1070	758	545	684	1456	3458	1100	2856	1969	463
3881	3873	3873	0	1194	181	3266	2794	3860	1010	3120	3604	989	3511	2893
3889	1004	1004	0	2008	915	2603	235	2273	1323	3432	1047	690	2941	2226
3889	2015	2015	0	3403	21	1745	845	1045	3435	3445	1007	69	1867	2014
3911	3187	3187	0	1549	908	92	2277	2930	856	390	3452	3148	1990	2385
3923	2385	2385	0	3804	2275	931	2184	2609	3204	3471	2210	2161	1797	3034
3931	1522	1522	0	3386	3040	3128	657	667	2230	233	2077	3478	2737	3202
3931	2753	2753	0	642	1068	490	3350	2033	1092	675	1515	2951	3862	384
3931	3725	3725	0	350	1651	872	3363	2061	861	2668	2277	1244	417	1098
3943	1466	1466	0	1627	187	1019	611	647	732	3	2761	2777	3808	1071
3943	1481	1481	0	421	3146	3555	1461	1406	3934	3048	1423	1888	345	3541
3947	1793	1793	0	2817	3362	3685	538	265	513	1522	3254	3011	642	1892
4003	1499	1499	0	1887	207	3215	2466	2265	949	635	653	2687	2735	3461
4003	1998	1998	0	3873	1656	2231	702	2250	3414	1546	1751	1306	1419	1870
4007	3032	3032	0	1913	816	1171	1516	3209	3982	2935	3939	821	1439	1424
4013	2534	2534	0	2459	3837	2675	1682	1607	1760	2540	2798	1197	2845	364
4027	2203	2203	0	3213	1115	1246	864	2700	657	3336	2090	3102	2679	2619
4049	192	192	0	392	1231	775	2575	3483	2238	338	2403	1683	777	657
4049	572	572	0	2977	3976	798	413	2458	1728	3532	3209	162	2482	3812
4049	703	703	0	3987	1015	349	1523	1359	2357	1837	2776	3972	2205	559
4051	1751	1751	0	2881	2417	562	1373	949	610	744	747	2136	1795	3123
4057	2883	2883	0	1868	2137	2104	3461	3915	2646	2258	3143	783	492	247
4073	613	613	0	3150	2747	2056	1661	2011	546	3337	1935	3121	142	3425
4091	2893	2893	0	3032	156	3795	3783	1441	2531	2936	2906	2373	410	2369
4099	4058	4058	0	3677	1978	1121	3331	3467	2703	2470	2622	2585	3756	630
4111	3546	3546	0	1485	3594	2	3399	2313	1263	144	436	1743	1297	324
4111	3557	3557	0	176	3029	454	3430	3912	1840	296	3942	3325	2259	2106
4129	2692	2692	0	3253	2194	1144	1480	4007	2048	27	729	3634	2608	2682
4129	3719	3719	0	3034	519	115	1301	2833	2545	1651	3955	2714	909	3859
4133	1411	1411	0	3036	1749	2487	2239	570	183	562	3754	229	2575	3118
4139	1857	1857	0	1126	4049	2560	1515	389	1519	1362	3212	1873	3237	1193
4153	363	363	0	3910	3227	2872	4028	3320	3282	3181	2834	2646	923	2569
4153	1795	1795	0	2879	3005	2120	2756	3162	1924	2804	1438	1992	1247	786
4177	2574	2574	0	2537	3897	940	3844	3584	1406	2650	1169	887	2878	3704
4201	1254	1254	0	3883	1037	4157	2641	2903	1520	4007	2211	3819	3676	3826
4229	1029	1029	0	3131	3345	1591	3515	2556	2936	1596	1978	4090	1696	511
4229	3732	3732	0	3043	1570	1416	4042	2848	3849	214	1262	1342	2508	24
4231	4098	4098	0	1837	51	349	152	615	2260	1265	4193	2876	3061	2596
4241	1679	1679	0	4029	3598	715	2953	2126	2200	3920	209	1481	2474	1679
4259	656	656	0	138	1964	1773	2051	3721	2233	1087	1038	1669	2898	269
4271	494	494	0	4015	1418	2049	672	462	1449	1378	2021	1196	1999	1421
4271	1277	1277	0	1150	3244	72	2098	3815	3042	3107	3108	3773	3330	374
4283	2690	2690	0	1846	3096	2129	2855	2285	3903	1436	370	3563	2331	2317
4283	3485	3485	0	1968	3493	2439	2433	4236	4144	2166	1155	4117	60	1203
4289	1323	1323	0	995	1993	1572	2673	2330	501	1254	3682	1553	3149	4072
4297	322	322	0	4296	703	197	587	2232	1967	326	2381	1511	101	3963
4297	1173	1173	0	2166	3615	1051	1616	133	1939	3034	3487	3568	727	502
4327	3251	3251	0	2441	1109	1086	2081	3461	1690	1909	1266	998	272	1105
4349	2376	2376	0	893	159	3268	1993	2428	4056	1707	3540	1763	3083	3279
4373	1850	1850	0	3683	432	30	2814	530	1971	4108	3173	441	471	228
4373	3070	3070	0	1479	3366	2436	3950	270	877	2659	969	2613	2593	2055
4391	2336	2336	0	3585	445	2708	3252	3585	4054	2026	4342	1086	2001	2604
4391	2489	2489	0	2914	501	4230	2335	1075	4185	1412	1296	2544	2803	3757
4391	2837	2837	0	2702	3720	1225	704	1521	4251	1735	3005	3568	80	4228
4391	3751	3751	0	4159	3964	1389	1818	2890	641	39	2649	160	4025	3611
4397	1196	1196	0	2493	2796	1684	1278	731	4305	2242	4155	3337	967	3368

References:

[1] http://go.helms-net.de/math/expdioph/Fermat-quotients.pdf
A directory with many more references:
http://go.helms-net.de/math/expdioph/fermatquotient/directory/index.htm

[2] The question asked in the math-discussion-forum math.stackexchange.com:
http://math.stackexchange.com/questions/594708#comment1253845_594708

[3] Richard Fischer's extensive compilation of informations about Fermat-quotients
http://www.fermatquotient.com
the list for degree 3
http://www.fermatquotient.com/FermatQuotienten/FermatQ3