M100 931 Mersenne number exponent details

is 2 ¹⁰⁰⁹³¹ - 1

has 30384 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	294.3983	74.6269%	1000000000	6734439121410	1,185.3149	25.4949%	1,479.7132	81.0957%
Target	2⁴⁴	0.0000	61.3636%	1200	18000	0.0000	4.1559%	0.0000	62.9693%
Difference	+23	+294.3983	+13.2632%	+999998800	+6734439103410	+1,185.3149	+21.3390%	+1,479.7132	+18.1264%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
100931	118896719	9	26.825	589 19 × 31	-	19	31	9.987e-11	6.333e-8	1.246e-7
100931	746591144050313	15	49.407	3698522476 2² × 11 × 61 × 67 × 131 × 157	2008-08-26	131	157	0.0015	4.267e-7	8.591e-7
100931	130178939820700909561	21	66.819	644890766071380 2² × 3 × 5 × 107 × 1069 × 2473 × 37997	2008-08-26	2473	37997	279.01	1.420e-5	1.622e-5
100931	529819870428377847116767	24	78.810	2624663732789617893 3⁴ × 11 × 17 × 173279443638319	2011-01-03	81	173279443638319	1,130,725	30,420	56,816

exponent	prime factors	composite factor	digits	bits*
100931	118896719 746591144050313	88767237462038586623047	23	76.232
100931	118896719 130178939820700909561	15477848827579786427118630359	29	93.644
100931	118896719 529819870428377847116767	62993844254939250514467206187473	32	105.635
100931	746591144050313 130178939820700909561	97190443611993939950186452646742593	35	116.226
100931	746591144050313 529819870428377847116767	395558823203711214084027150733433898071	39	128.217
100931	118896719 746591144050313 130178939820700909561	11555624863620588507960192657946560345252367	44	143.052
100931	130178939820700909561 529819870428377847116767	68971389028307353192825803004726678273709287	44	145.629
100931	118896719 746591144050313 529819870428377847116767	47030646250422331978097418529123734084022329049	47	155.042
100931	118896719 130178939820700909561 529819870428377847116767	82004718603383424182011623158023435385126181841293 53	52	172.454
100931	746591144050313 130178939820700909561 529819870428377847116767	51493428241383192700025096719208172766265375068739 463356831	59	195.036
100931	118896719 746591144050313 130178939820700909561 529819870428377847116767	61223996679624016337777352175715160198941069789775 21658947932137489	67	221.861

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	200000000	5000000000	12	-	skipped known factor: 118896719 skipped known factor: 746591144050313 skipped known factor: 130178939820700909561	-	-	1.487	-	-	13.401%
2021-12-17	Seth_Tr	Manual testing	1000000000	6734439121410		-	skipped known factor: 118896719 skipped known factor: 746591144050313 skipped known factor: 130178939820700909561	-	-	1,185	-	-	25.495%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26	ANONYMOUS	Manual testing	?	?	746591144050313	49.407	15	0.001	0.000	0.001
2018-11-01	J.R. Allen	Manual testing	2⁵²	2⁵⁷		-	-	0.184	-	-
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	118896719	26.825	9	9.98692e-11	0.000	2.13112e-10
2022-04-13	LordJulius	Manual testing	2¹	2⁵⁷	746591144050313	49.407	15	0.001	0.000	0.003
2018-11-01	J.R. Allen	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁷	2⁵⁸		-	-	0.190	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁸	2⁵⁹		-	-	0.380	-	-
2018-11-01	J.R. Allen	Manual testing	2⁵⁹	2⁶⁰		-	-	0.761	-	-
2022-04-13	LordJulius	Manual testing	2⁵⁹	2⁶⁰		-	-	0.761	-	-
2022-04-13	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	1.522	-	-
2022-04-13	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	3.043	-	-
2022-10-31	LordJulius	Manual testing	2⁶²	2⁶³		-	-	9.73	-	-
2022-10-31	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	19.45	-	-
2022-10-31	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	37.02	-	-
2022-11-01	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	74.04	-	-
2022-11-01	LordJulius	Manual testing	2⁶⁶	2⁶⁷	130178939820700909561	66.819	21	132.7	0.000	269.4

ECM factoring results:

Total ECM effort:	12.734 GHz-days
Estimated T-Level:	30.766

Digits	B1	Complete	FacMiss
20	11000	82.951	0.000%
25	50000	13.036	0.000%
30	250000	1.560	21.008%
35	1000000	0.153	85.798%
40	3000000	0.013	98.726%

ECM Summary

B1	B2	factor	curves	GHz-days
		130178939820700909561	1	0.00000e+0
		529819870428377847116767	1	0.00000e+0
50000	5000000		280	0.650
250000	25000000		585	6.791
1000000	100000000		114	5.293

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-08-26	ANONYMOUS	Manual testing			130178939820700909561	66.819		1		1	-
2010-01-15	Rob_Dee	twopc	50000	5000000						1	0.002
2010-04-19	James Hintz	NEW_OMFG	50000	5000000						11	0.026
2011-01-03	Rob_Dee	twopc			529819870428377847116767	78.810		1		1	-
2014-04-11	TJAOI	Manual testing	50000	5000000						37	0.086
2014-06-26	TJAOI	Manual testing	50000	5000000						231	0.536
2017-02-08	kkmrkkblmbrbk	kel1	250000	25000000						585	6.791
2019-01-25	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-01-31	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-02-06	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-12	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-18	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-02-24	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-08	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-03-13	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-03-20	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-03-27	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-02	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-08	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-04-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-04-25	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-02	Niels_Mache_Nextcloud	SuperDry-X	1000000	100000000						3	0.139
2019-05-10	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-16	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-05-28	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-08	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-06-19	Niels_Mache_Nextcloud	SuperDry-JP	1000000	100000000						3	0.139
2019-07-05	Niels_Mache_Nextcloud		1000000	100000000						3	0.139
2019-07-25	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-02	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-09	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-08-16	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-23	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-08-31	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-07	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139
2019-09-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-09-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-07	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-14	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-22	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-10-29	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-05	Niels_Mache_Nextcloud	SuperDry-Y	1000000	100000000						3	0.139
2019-11-12	Niels_Mache_Nextcloud	SuperDry3	1000000	100000000						3	0.139

Lucas-Lehmer results:
No L-L results for M100931

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

PRP

118896719

746591144050313

130178939820700909561

529819870428377847116767

98CF924E87FAD325

2017-09-21

Oliver Kruse

Manual testing

118896719

746591144050313

130178939820700909561

529819870428377847116767

98CF924E87FAD325

2017-10-09

Chang Chia-Tche

homura

98CF924E87FAD3__

2017-10-13

kkmrkkblmbrbk

Manual testing

118896719

746591144050313

130178939820700909561

529819870428377847116767

98CF924E87FAD3__

2020-04-17

Oliver Kruse

AddPrpType5

118896719

746591144050313

130178939820700909561

529819870428377847116767

392AB9DAA3BB85__

2022-04-15

LordJulius

WhiteBox

118896719

746591144050313

130178939820700909561

529819870428377847116767

392AB9DAA3BB858E

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 = 6734439121410 (P-1 stage 2)

B1 = 1000000000 (P-1 stage 1)

B1 = 200000000, B2 = 5000000000 (P-1 stage 2)

B1 = 200000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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: 2023-03-23T17:39:31+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