M31 151 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	953.8672	77.6119%	3000000000	920287779501090	40,049.3552	31.9918%	41,003.2224	84.7743%
Target	2⁴⁴	0.0001	65.9091%	500	50000	0.0000	1.7781%	0.0001	66.5153%
Difference	+23	+953.8671	+11.7028%	+2999999500	+920287779451090	+40,049.3552	+30.2136%	+41,003.2223	+18.2590%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
31151	62303	5	15.927	1 1	-	1	1	1.402e-13	7.987e-10	1.626e-9
31151	1308343	7	20.319	21 3 × 7	2008-08-26	3	7	4.505e-12	2.570e-9	4.877e-9
31151	45667367	8	25.445	733 733	2008-08-26	1	733	1.663e-10	3.265e-8	5.984e-8
31151	1060322784463	13	39.948	17019081 3² × 59 × 32051	2008-08-26	59	32051	4.194e-6	1.439e-6	2.605e-6
31151	158183593260403411492113979070765956490038975001	48	156.792	2538980983923524308884369347224261765112500 2² × 5⁵ × 191 × 857 × 10789 × 2387767 × 84656639 × 568985350414651	2022-10-21	84656639	568985350414651	5.477e+12	24,760	46,245

exponent	prime factors	composite factor	digits	bits*
31151	62303 1308343	81513693929	11	36.246
31151	62303 45667367	2845213966201	13	41.372
31151	1308343 45667367	59748579942881	14	45.764
31151	62303 1060322784463	66061290440398289	17	55.875
31151	1308343 1060322784463	1387265892792674809	19	60.267
31151	62303 1308343 45667367	3722515776181314943	19	61.691
31151	45667367 1060322784463	48422149736533718921	20	65.392
31151	62303 1308343 1060322784463	86430826918662018625127	23	76.194
31151	62303 45667367 1060322784463	3016845195035260289935063	25	81.319
31151	1308343 45667367 1060322784463	63352780652745735414257903	26	85.712
31151	62303 1308343 45667367 1060322784463	3947068293008017553514510130609	31	101.639
31151	62303 158183593260403411492113979070765956490038975001	98553124109029137461931772380459313871988982594873 03	52	172.719
31151	1308343 158183593260403411492113979070765956490038975001	20695839695709598060182687971938314381204706266973 3343	54	177.112
31151	45667367 158183593260403411492113979070765956490038975001	72238282068015691606623866880549879061366417156744 92367	55	182.237
31151	62303 1308343 158183593260403411492113979070765956490038975001	12894129005617950879435620087156728008921968145512 396468929	59	193.039
31151	1060322784463 158183593260403411492113979070765956490038975001	16772566806223358591598266785448106430770563209645 4768209463	60	196.740
31151	62303 45667367 158183593260403411492113979070765956490038975001	45006616876835816341674867782588991151603118881166 7897941201	60	198.164
31151	1308343 45667367 158183593260403411492113979070765956490038975001	94512450675713854003685089866099270420785322322107 12366917881	61	202.556
31151	62303 1060322784463 158183593260403411492113979070765956490038975001	10449812297281339103323468155337733749562983996505 421423754173289	65	212.667
31151	1308343 1060322784463 158183593260403411492113979070765956490038975001	21944270372954687649807451160873531911953650981397 1920803473449809	66	217.059
31151	62303 1308343 45667367 158183593260403411492113979070765956490038975001	58884092144490002459915921539275828450261879366342 4012596084739943	66	218.483
31151	45667367 1060322784463 158183593260403411492113979070765956490038975001	76595896387182000077512116585496893582905940289157 79298721479693921	67	222.185
31151	62303 1308343 1060322784463 158183593260403411492113979070765956490038975001	13671938770461959046459536296759036587104483170939 892581818806343450127	71	232.986
31151	62303 45667367 1060322784463 158183593260403411492113979070765956490038975001	47721541326106001508292373996262129608957887978353 9797648244349370360063	72	238.112
31151	1308343 45667367 1060322784463 158183593260403411492113979070765956490038975001	10021370486689485952741243514981876224093990663573 757435027156907183682903	74	242.504
31151	62303 1308343 45667367 1060322784463 158183593260403411492113979070765956490038975001	62436144543221504331363769471391583438972790031263 5809474496956788264995905609	78	258.431

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-10-09	kkmrkkblmbrbk	Manual testing	200000000	5000000000	12	-	skipped known factor: 62303 skipped known factor: 1308343 skipped known factor: 45667367 skipped known factor: 1060322784463	-	-	0.369	-	-	12.357%
2022-09-25	nordi	sweet16_ccx3	3000000000	3000000000		-	skipped known factor: 62303 skipped known factor: 1308343 skipped known factor: 45667367 skipped known factor: 1060322784463	-	-	2.396	-	-	11.661%
2022-10-21	nordi	sweet16_30.8b14	3000000000	920287779501090			158183593260403411492113979070765956490038975001	48	156.792	40,049	3.43180e-5	80,099	31.992%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-08-26	ANONYMOUS	Manual testing	?	?	1060322784463	39.948	13	1.84267e-6	0.000	1.13469e-5
2008-08-26	ANONYMOUS	Manual testing	?	?	1308343	20.319	7	2.03830e-14	0.000	1.31101e-13
2008-08-26	ANONYMOUS	Manual testing	?	?	45667367	25.445	8	2.27669e-11	0.000	1.46433e-10

ECM factoring results:

Total ECM effort:	574.282 GHz-days
Estimated T-Level:	36.146

Digits	B1	Complete	FacMiss
20	11000	416.490	0.000%
25	50000	84.773	0.000%
30	250000	14.252	0.000%
35	1000000	1.965	14.016%
40	3000000	0.229	79.517%
45	11000000	0.023	97.707%
50	44000000	0.002	99.791%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	0.161
250000	25000000	585	1.681
1000000	100000000	1,511	17.37
3000000	11486324850	50	22.63
3000000	22329437130	2	1.716
3000000	41351084775	150	235.4
4127829	41351084775	50	78.90
4486870	114864374625	50	216.5

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-03-30	Matthias Wurtinger	WUR_E6600	50000	5000000						30	0.017
2010-04-13	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-13	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-14	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-15	James Hintz	14_091909	50000	5000000						11	0.006
2010-04-23	James Hintz	home2	50000	5000000						163	0.094
2011-01-20	James Hintz	NEW_OMFG	250000	25000000						4	0.011
2011-03-17	James Hintz	17_051310	250000	25000000						11	0.032
2015-06-16	James Hintz	08_04_2014	250000	25000000						570	1.638
2015-06-16	James Hintz	08_04_2014	1000000	100000000						11	0.126
2017-05-09	nordi	nordiputer	1000000	100000000						1500	17.24
2022-12-20	nordi	sweet16_30.9b3	3000000	11486324850						50	22.63
2023-04-17	carlos56	Manual testing	3000000	22329437130						1	0.858
2023-04-17	carlos56	Manual testing	3000000	22329437130						1	0.858
2023-09-20	Stef42	z8g4	3000000	41351084775						50	78.46
2023-09-21	Stef42	z8g4	3000000	41351084775						50	78.46
2023-09-26	Stef42	z8g4	3000000	41351084775						50	78.46
2023-10-03	Stef42	z8g4	4127829	41351084775						50	78.90
2023-10-12	Stef42	z8g4	4486870	114864374625						50	216.5

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

62303

1308343

45667367

1060322784463

8DEC35D8A13845__

2017-09-21

Oliver Kruse

Manual testing

62303

1308343

45667367

1060322784463

8DEC35D8A13845__

2017-10-12

kkmrkkblmbrbk

Manual testing

62303

1308343

45667367

1060322784463

8DEC35D8A13845__

2020-04-17

Oliver Kruse

Manual testing

62303

1308343

45667367

1060322784463

C036968FC41641__

2022-05-12

Jorge Coveiro

Manual testing

62303

C036968FC41641EC

2022-10-21

Kevin_9611

62303

1308343

45667367

1060322784463

158183593260403411492113979070765956490038975001

C036968FC41641EC

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 = 3000000000, B2 = 920287779501090 (P-1 stage 2)

B1 = 3000000000 (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

10¹⁰

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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