M10 657 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	2,788.2066	79.1045%	100000000000	120443211520241610	1,247,541.9951	40.3792%	1,250,330.2017	87.5419%
Target	2⁴⁴	0.0002	68.1818%	500	10000	0.0000	1.2887%	0.0002	68.5919%
Difference	+23	+2,788.2064	+10.9227%	+99999999500	+120443211520231610	+1,247,541.9951	+39.0905%	+1,250,330.2015	+18.9501%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
10657	2216657	7	21.080	104 2³ × 13	-	8	13	2.681e-11	1.573e-9	3.095e-9
10657	39041962129	11	35.184	1831752 2³ × 3² × 13 × 19 × 103	2008-08-26	19	103	6.370e-7	4.482e-9	7.351e-9
10657	874071793921	12	39.669	41009280 2⁷ × 3 × 5 × 13 × 31 × 53	2008-08-26	128	128	1.009e-5	2.433e-8	4.952e-8
10657	2166536299513	13	40.979	101648508 2² × 3 × 13 × 17 × 38329	2008-08-26	17	38329	2.531e-5	4.001e-7	7.414e-7
10657	67867710628343	14	45.948	3184184603 337 × 9448619	2008-08-26	337	9448619	0.0006	9.793e-5	0.0002
10657	277342730769618156583567703	27	87.842	13012232840837860400843 23 × 1380317 × 19947391 × 20547503	2009-06-01	19947391	20547503	5.095e+9	0.0038	0.0077

exponent	prime factors	composite factor	digits	bits*
10657	2216657 39041962129	86542638646982753	17	56.264
10657	2216657 874071793921	1937517360497542097	19	60.749
10657	2216657 2166536299513	4802467854069588041	19	62.058
10657	2216657 67867710628343	150439435838290909351	21	67.028
10657	39041962129 874071793921	34125477876290774417809	23	74.853
10657	39041962129 2166536299513	84585828156690347143177	23	76.163
10657	874071793921 2166536299513	1893708269910292868660473	25	80.647
10657	39041962129 67867710628343	2649688588133698200022247	25	81.132
10657	874071793921 67867710628343	59321251578227084117702903	26	85.617
10657	2166536299513 67867710628343	147037858641149343274896959	27	86.926
10657	2216657 39041962129 874071793921	75644479412825079148657244513	29	95.933
10657	2216657 39041962129 2166536299513	187497768084324754827353299289	30	97.243
10657	2216657 874071793921 2166536299513	4197701692454540059366318098761	31	101.727
10657	2216657 39041962129 67867710628343	5873450756706679050966713968279	31	102.212
10657	2216657 874071793921 67867710628343	131494867559638113599094963855271	33	106.697
10657	2216657 2166536299513 67867710628343	325932498621914179815703268446063	33	108.006
10657	2216657 277342730769618156583567703	614773705559589474118061433828871	33	108.922
10657	39041962129 874071793921 2166536299513	73934086557211764405540957825227017	35	115.832
10657	39041962129 874071793921 67867710628343	2316018057562023299085454117399360487	37	120.801
10657	39041962129 2166536299513 67867710628343	5740646508597008061171747909655265711	37	122.111
10657	39041962129 277342730769618156583567703	10828004391460875093126442284233519687	38	123.026
10657	874071793921 2166536299513 67867710628343	128521644876771817865560221999557586239	39	126.595
10657	874071793921 277342730769618156583567703	242417458214749067089172098711567333463	39	127.511
10657	2166536299513 277342730769618156583567703	600873093618438763492579369800921428639	39	128.820
10657	67867710628343 277342730769618156583567703	18822616196746885341722344994758811206129	41	133.790
10657	2216657 39041962129 874071793921 2166536299513	163886510505649358051893202949994243822169	42	136.912
10657	2216657 39041962129 874071793921 67867710628343	5133817639421261880080865467512114219031959	43	141.881
10657	2216657 39041962129 2166536299513 67867710628343	12725044267807118097852783206172712325148127	44	143.191
10657	2216657 39041962129 277342730769618156583567703	24001971730362489001304380174442221048826359	44	144.106
10657	2216657 874071793921 2166536299513 67867710628343	284888403767610387474419125016873320439783023	45	147.675
10657	2216657 874071793921 277342730769618156583567703	537356355673931022806682956813686710692093191	45	148.591
10657	2216657 2166536299513 277342730769618156583567703	1331929549080967614167170508124801091242639823	46	149.900
10657	2216657 67867710628343 277342730769618156583567703	41723283950832360620926228089047082171744290753	47	154.870
10657	39041962129 874071793921 2166536299513 67867710628343	5017737192035712184881687800675559936697689542831	49	161.780
10657	39041962129 874071793921 277342730769618156583567703	9464453223028673026533537343860461527295960422727	49	162.695
10657	39041962129 2166536299513 277342730769618156583567703	23459264565386157780382871528294260686228414012431	50	164.005
10657	874071793921 2166536299513 277342730769618156583567703	52520622285792974708924389313336704576926091550351 9	51	168.489
10657	39041962129 67867710628343 277342730769618156583567703	73487186872209391051022901691844621059874923068864 1	51	168.974
10657	874071793921 67867710628343 277342730769618156583567703	16452317905377020355008549197459689453662532740141 809	53	173.459
10657	2166536299513 67867710628343 277342730769618156583567703	40779881242053454916963631790849492210477719925315 177	53	174.768
10657	2216657 39041962129 874071793921 2166536299513 67867710628343	11122602270886305664603287435182084662600490408943 135967	56	182.860
10657	2216657 39041962129 874071793921 277342730769618156583567703	20979446487999069264976751288029699067711281742760 763639	56	183.775
10657	2216657 39041962129 2166536299513 277342730769618156583567703	52001143013715184346990154853294171009953017519553 263167	56	185.085
10657	2216657 874071793921 2166536299513 277342730769618156583567703	11642020503415899793936021004213299955737525931772 83915983	58	189.569
10657	2216657 39041962129 67867710628343 277342730769618156583567703	16289588719059105213898727219553922218471916734505 90893137	58	190.054
10657	2216657 874071793921 67867710628343 277342730769618156583567703	36469145651179309809072185638393402845287228836164 521912513	59	194.539
10657	2216657 2166536299513 67867710628343 277342730769618156583567703	90395009214366485215871853154609062854800911216489 364303289	59	195.848
10657	39041962129 874071793921 2166536299513 277342730769618156583567703	20505081462734427333200808058957439347180094335408 257764231951	62	203.674
10657	39041962129 874071793921 67867710628343 277342730769618156583567703	64233077259599823416710591323845453865399330358683 9105067551361	63	208.643
10657	39041962129 2166536299513 67867710628343 277342730769618156583567703	15921265790773684690617029520486463236203516383224 23848822931833	64	209.952
10657	874071793921 2166536299513 67867710628343 277342730769618156583567703	35644543953127000965046299733743121528924176367522 042901717639017	65	214.437
10657	2216657 39041962129 874071793921 2166536299513 277342730769618156583567703	45452732359940507489130903589544420631002186369243 062430889103807807	68	224.754
10657	2216657 39041962129 874071793921 67867710628343 277342730769618156583567703	14238270033903276577541544923214129222891448343488 92010121723197220177	70	229.723
10657	2216657 39041962129 2166536299513 67867710628343 277342730769618156583567703	35291985263979023585249072805792962137773178015488 69081460293608142281	70	231.032
10657	2216657 874071793921 2166536299513 67867710628343 277342730769618156583567703	79011727865506638578176635628899826538940478014302 309052392716550506169	71	235.517
10657	39041962129 874071793921 2166536299513 67867710628343 277342730769618156583567703	13916329351234603228046840869363817341465022718533 12384541573331553006787193	76	249.621
10657	2216657 39041962129 874071793921 2166536299513 67867710628343 277342730769618156583567703	30847728870719641887672626140961391256679832864195 47870380770316400293365878873801	82	270.701

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-09-07	kkmrkkblmbrbk	Manual testing	100000000	10000000000	12	-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	0.122	-	-	12.094%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	0.076	-	-	7.663%
2022-03-05	Jocelyn Larouche	Manual testing	1000000000	6419160908160		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	66.67	-	-	22.814%
2022-03-05	Jocelyn Larouche	Manual testing	1000000000	12500472934950		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	129.7	-	-	23.751%
2022-03-05	Jocelyn Larouche	Manual testing	1000000000	104918137544220		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	1,087	-	-	26.649%
2022-03-05	Jocelyn Larouche	Manual testing	1000000000	1002689751483420		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	10,386	-	-	29.577%
2022-11-08	-Anonymous-	2650v4	100000000000	120443211520241610		-	skipped known factor: 2216657 skipped known factor: 39041962129 skipped known factor: 874071793921 skipped known factor: 2166536299513 skipped known factor: 67867710628343 skipped known factor: 277342730769618156583567703	-	-	1,247,542	-	-	40.379%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2003-04-03	ANONYMOUS	v4_computers	?	?	2216657 39041962129	56.264	17	0.399	2.98796e-6	0.854
2008-08-26	ANONYMOUS	Manual testing	?	?	2166536299513	40.979	13	1.15668e-5	0.000	0.002
2008-08-26	ANONYMOUS	Manual testing	?	?	39041962129	35.184	11	2.07506e-7	0.000	3.29753e-5
2008-08-26	ANONYMOUS	Manual testing	?	?	67867710628343	45.948	14	0.000	2.98796e-6	0.000
2008-08-26	ANONYMOUS	Manual testing	?	?	874071793921	39.669	12	3.21300e-6	0.000	0.000

ECM factoring results:

Total ECM effort:	38.467 GHz-days
Estimated T-Level:	40.562

Digits	B1	Complete	FacMiss
20	11000	1,084.888	0.000%
25	50000	269.328	0.000%
30	250000	51.642	0.000%
35	1000000	7.974	0.034%
40	3000000	1.017	36.178%
45	11000000	0.112	89.374%
50	44000000	0.011	98.929%

ECM Summary

B1	B2	factor	curves	GHz-days
		277342730769618156583567703	1	0.00000e+0
50000	5000000		213	0.029
250000	25000000		2	0.001
350000	35000000		6	0.006
400000	40000000		1	0.001
950000	95000000		5	0.013
1000000	100000000		1,389	3.800
3000000	300000000		4,218	34.62

ECM Details

										GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-04-03	Matthias Wurtinger	WUR_E6600	50000	5000000						50	0.007
2009-06-01	Rob_Dee	twopc			277342730769618156583567703	87.842		1		1	-
2009-06-02	Rob_Dee	twopc	50000	5000000						88	0.012
2009-07-11	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-12	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-12	Rob_Dee	twopc	50000	5000000						4	0.001
2009-07-13	Rob_Dee	twopc	50000	5000000						6	0.001
2009-07-26	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-28	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-28	Rob_Dee	twopc	250000	25000000						2	0.001
2009-07-28	Rob_Dee	twopc	50000	5000000						19	0.003
2009-07-29	Rob_Dee	twopc	950000	95000000						1	0.003
2009-07-30	Rob_Dee	twopc	950000	95000000						1	0.003
2009-07-31	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-01	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-02	Rob_Dee	twopc	400000	40000000						1	0.001
2009-08-02	Rob_Dee	twopc	350000	35000000						3	0.003
2009-08-04	Rob_Dee	twopc	950000	95000000						1	0.003
2009-08-05	Rob_Dee	twopc	350000	35000000						3	0.003
2009-08-08	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-09	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-11	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-13	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-16	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-17	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-18	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-19	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-20	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-21	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-22	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-25	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-26	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-27	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-28	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-29	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-30	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-30	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-08-31	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-01	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-02	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-03	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-04	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-05	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-06	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-08	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-11	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-12	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-12	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-14	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-15	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-16	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-17	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-18	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-19	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-20	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-21	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-22	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-23	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-24	Rob_Dee	twopc	1000000	100000000						1	0.003
2009-09-25	Rob_Dee	twopc	1000000	100000000						1	0.003
2010-01-11	Rob_Dee	twopc	1000000	100000000						1	0.003
2010-01-21	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-01-22	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-01-23	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-01-25	Rob_Dee	twopc	1000000	100000000						10	0.027
2010-05-12	James Hintz	home2	1000000	100000000						1300	3.556
2011-01-01	James Hintz	home2	3000000	300000000						3	0.025
2011-04-17	James Hintz	lappy_010411	3000000	300000000						11	0.090
2011-04-21	James Hintz	17_051310	3000000	300000000						11	0.090
2016-11-18	James Hintz	11_04_2016	3000000	300000000						100	0.821
2019-02-09	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-02-12	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-13	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-15	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-17	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-18	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-20	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-21	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-02-23	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-02-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-02-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-03-01	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-03-03	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-04	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-06	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-07	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-08	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-09	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-10	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-03-11	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-13	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-14	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-17	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-03-19	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-20	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-22	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-24	Niels_Mache_Nextcloud	SuperDry-JP	3000000	300000000						3	0.025
2019-03-26	Niels_Mache_Nextcloud	SuperDry-X	3000000	300000000						3	0.025
2019-03-27	Niels_Mache_Nextcloud	SuperDry3	3000000	300000000						3	0.025
2019-04-01	alex	newwork	3000000	300000000						4000	32.83

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