M100 537 Mersenne number exponent details

is 2 ¹⁰⁰⁵³⁷ - 1

has 30265 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	295.5521	74.6269%	1000000000	6550372728900	1,153.0010	25.4491%	1,448.5531	81.0841%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1522%	0.0000	62.9679%
Difference	+23	+295.5520	+13.2632%	+999998800	+6550372710900	+1,153.0010	+21.2969%	+1,448.5530	+18.1162%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100537	6524449153	10	32.603	32448 2⁶ × 3 × 13²	-	169	169	5.824e-9	5.446e-7	1.108e-6
100537	8910884448107040315479713	25	82.882	44316442941936999888 2⁴ × 3 × 161881 × 5703320512951	2014-05-22	161881	5703320512951	16,675,870	1,001.3	1,870.1

exponent	prime factors	composite factor	digits	bits*
100537	6524449153 8910884448107040315479713	58138612489932851639668466271533089	35	115.485

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: 6524449153	-	-	0.656	-	-	11.728%
2021-12-17	Seth_Tr	Manual testing	1000000000	6550372728900		-	skipped known factor: 6524449153 skipped known factor: 8910884448107040315479713	-	-	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	6524449153	32.603	10	5.82416e-9	0.000	1.24334e-8
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		-	-	3.055	-	-
2022-10-23	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.76	-	-
2022-10-23	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.53	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.16	-	-
2022-10-23	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.33	-	-
2022-10-23	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
		8910884448107040315479713	1	0.00000e+0
50000	5000000		281	0.652
250000	25000000		585	6.790
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
2014-05-22	TJAOI	Manual testing			8910884448107040315479713	82.882		1		1	-
2014-05-26	TJAOI	Manual testing	50000	5000000						231	0.536
2016-09-16	TJAOI	Manual testing	250000	25000000						1	0.012
2017-01-23	kkmrkkblmbrbk	kel1	250000	25000000						584	6.779
2019-01-24	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-01-30	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-05	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-17	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-01	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-07	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-11	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-18	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-13	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-23	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-04-30	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-14	Niels_Mache_Nextcloud	SuperDry-JP	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
2019-08-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-21	Niels_Mache_Nextcloud	SuperDry3	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	SuperDry3	1000000	100000000						3	0.139
2019-09-19	Niels_Mache_Nextcloud	SuperDry-Y	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	SuperDry3	1000000	100000000						3	0.139
2019-11-02	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-11-10	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100537

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Doppelherz

6524449153

8910884448107040315479713

F00C78E9796797__

2017-09-21

Oliver Kruse

Manual testing

6524449153

8910884448107040315479713

F00C78E9796797__

2017-09-22

Oliver Kruse

Manual testing

6524449153

8910884448107040315479713

F00C78E9796797__

2017-11-06

kkmrkkblmbrbk

c4.xlarge

6524449153

8910884448107040315479713

F00C78E9796797__

2020-04-17

Oliver Kruse

AddPrpType5

6524449153

8910884448107040315479713

4F1C12FBDEBD0F__

2022-04-15

LordJulius

WhiteBox

6524449153

8910884448107040315479713

4F1C12FBDEBD0F79

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 = 6550372728900 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

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

B1 = 100000000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁹

2⁵⁸

2⁵⁷

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=30.77 ~= 86-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-03-25T13:08:14+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