M100 517 Mersenne number exponent details

is 2 ¹⁰⁰⁵¹⁷ - 1

has 30259 decimal digits

takes 0.000 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	295.6109	74.6269%	1000000000	6551302697940	1,153.1643	25.4491%	1,448.7751	81.0841%
Target	2⁴⁴	0.0000	61.3636%	1200	144000	0.0000	4.1521%	0.0001	62.9678%
Difference	+23	+295.6108	+13.2632%	+999998800	+6551302553940	+1,153.1642	+21.2970%	+1,448.7751	+18.1163%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100517	999459033164191	15	49.828	4971592035 3² × 5 × 110479823	-	9	110479823	0.0009	0.0194	0.0362
100517	3761696432449035921728660089	28	91.603	18711742453759244315532 2² × 3 × 37 × 73 × 211 × 229399 × 11927088049	2017-01-21	229399	11927088049	9.926e+9	2.0946	3.9108
100517	117245631774983322771883893206263	33	106.531	583212947934097330659907743 3 × 17 × 349 × 32766613176813154146857	2017-01-21	349	32766613176813154146857	1.377e+12	5.752e+12	1.074e+13

exponent	prime factors	composite factor	digits	bits*
100517	999459033164191 3761696432449035921728660089	3759661479432699963053429957962184365672999	43	141.432
100517	999459033164191 117245631774983322771883893206263	117182205776549582895480242241445275833108528233	48	156.359
100517	3761696432449035921728660089 117245631774983322771883893206263	44104247476818809246323870457680229998903259349456 5092937407	60	198.135
100517	999459033164191 3761696432449035921728660089 117245631774983322771883893206263	44080388541615537503008671481413512712238417293705 9369101242066921916792737	75	247.963

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-31	kkmrkkblmbrbk	Manual testing	100000000	2000000000	12	-	skipped known factor: 999459033164191	-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6551302697940		-	skipped known factor: 999459033164191 skipped known factor: 3761696432449035921728660089	-	-	1,153	-	-	25.449%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2018-10-25	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.185	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	999459033164191	49.828	15	0.001	0.000	0.002
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.191	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.382	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.764	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.528	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.056	-	-
2022-10-22	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.77	-	-
2022-10-22	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.53	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.17	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.34	-	-
2022-10-22	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	148.7	-	-

ECM factoring results:

Total ECM effort:	12.736 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.990	0.000%
25	50000	13.039	0.000%
30	250000	1.561	21.003%
35	1000000	0.153	85.797%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	0.652
250000	25000000		322	3.738
250000	25000000	3761696432449035921728660089	59	0.685
250000	25000000	117245631774983322771883893206263	204	2.368
1000000	100000000		114	5.293

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-28	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2010-01-29	Rob_Dee	twopc	50000	5000000						1	0.002
2014-04-11	TJAOI	Manual testing	50000	5000000						40	0.093
2014-05-19	TJAOI	Manual testing	50000	5000000						231	0.536
2017-01-21	kkmrkkblmbrbk	kel1	250000	25000000	117245631774983322771883893206263	106.531	204	2		204	2.368
2017-01-22	kkmrkkblmbrbk	kel1	250000	25000000	3761696432449035921728660089	91.603	59	2		59	0.685
2017-01-22	kkmrkkblmbrbk	kel1	250000	25000000						322	3.738
2019-01-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-18	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-29	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-24	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-27	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-07-30	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-06	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-13	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-21	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-28	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-12	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-27	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-04	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-11	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-19	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-26	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-09	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100517

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

999459033164191

3761696432449035921728660089

117245631774983322771883893206263

31BFF45DAD69AB45

2017-09-21

Oliver Kruse

Manual testing

999459033164191

3761696432449035921728660089

117245631774983322771883893206263

31BFF45DAD69AB45

2017-10-09

Chang Chia-Tche

homura

31BFF45DAD69AB__

2017-10-13

kkmrkkblmbrbk

Manual testing

999459033164191

3761696432449035921728660089

117245631774983322771883893206263

31BFF45DAD69AB__

2020-04-17

Oliver Kruse

AddPrpType5

999459033164191

3761696432449035921728660089

117245631774983322771883893206263

EA5300A8D05B81__

2022-04-15

LordJulius

WhiteBox

999459033164191

3761696432449035921728660089

117245631774983322771883893206263

EA5300A8D05B8185

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 1000000000, B2 = 6551302697940 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 100000000, B2 = 2000000000 (P-1 stage 2)

B1 = 100000000 (P-1 stage 1)

10⁰

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10¹⁵

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10²³

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.8

ECM T-Level=30.77 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

Last modified: 2023-06-05T21:50:05+00:00

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront