M8 761 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	3,391.6125	79.1045%	400000000	400000000	0.0707	7.5384%	3,391.6833	80.6797%
Target	2⁴⁴	0.0003	68.1818%	500	10000	0.0000	1.2134%	0.0003	68.5679%
Difference	+23	+3,391.6123	+10.9227%	+399999500	+399990000	+0.0707	+6.3250%	+3,391.6830	+12.1118%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8761	192743	6	17.556	11 11	-	1	11	1.998e-12	2.732e-10	3.599e-10
8761	21086064775471	14	44.261	1203405135 3 × 5 × 103 × 778903	-	103	778903	0.0003	7.521e-6	1.401e-5
8761	27521653946472839	17	54.611	1570691356379 31 × 50667463109	-	31	50667463109	0.2917	0.4881	0.9117
8761	252738375533197927	18	57.810	14424059783883 3 × 19 × 31 × 311 × 3307 × 7937	-	3307	7937	2.8758	6.293e-7	1.190e-6
8761	978770943064293241	18	59.764	55859544747420 2² × 3 × 5 × 337 × 5857 × 471673	-	5857	471673	12.181	5.523e-6	8.487e-6
8761	741360813207419388145717037710039122529073	42	139.089	42310284967892899677303791673897906776 2³ × 7 × 137849 × 633151 × 8656593143205309812301179	2018-06-05	633151	8656593143205309812301179	1.940e+13	8.339e+13	1.558e+14

exponent	prime factors	composite factor	digits	bits*
8761	192743 21086064775471	4064191383018606953	19	61.818
8761	192743 27521653946472839	5304606146605014407377	22	72.168
8761	192743 252738375533197927	48713552715395168043761	23	75.367
8761	192743 978770943064293241	188651247879041072150063	24	77.320
8761	21086064775471 27521653946472839	580323377843423364940934932169	30	98.873
8761	21086064775471 252738375533197927	5329257757740326426493857648617	31	102.072
8761	21086064775471 978770943064293241	20638427505802525383503967891511	32	104.025
8761	27521653946472839 252738375533197927	6955778110418371142367311716604753	34	112.422
8761	27521653946472839 978770943064293241	26937395187878348481816356337781199	35	114.375
8761	192743 21086064775471 27521653946472839	111853268815674949628810621631049567	36	116.429
8761	252738375533197927 978770943064293241	247372978169165632103539558821311407	36	117.574
8761	192743 21086064775471 252738375533197927	1027177128000143736421705604767386431	37	119.628
8761	192743 21086064775471 978770943064293241	3977912432750896149992705283313504673	37	121.581
8761	192743 27521653946472839 252738375533197927	1340677540336368109093302762193549907479	40	129.978
8761	192743 27521653946472839 978770943064293241	5191994360697236521430729969612961638857	40	131.931
8761	192743 252738375533197927 978770943064293241	47679409931259491428532525185896024519401	41	135.130
8761	192743 741360813207419388145717037710039122529073	142892107220037635129369938999346070593621117239	48	156.646
8761	21086064775471 27521653946472839 252738375533197927	146669987800085047747954934506999268649396413663	48	156.683
8761	21086064775471 27521653946472839 978770943064293241	568003659814063664041093301527871645726260169729	48	158.637
8761	21086064775471 252738375533197927 978770943064293241	5216122641376200098956731656801862110653226097697	49	161.836
8761	27521653946472839 252738375533197927 978770943064293241	68081135008801567659344938879198497348098720863744 73	52	172.186
8761	192743 21086064775471 27521653946472839 252738375533197927	28269613458551792358084077941682560037290612958647 609	53	174.240
8761	192743 21086064775471 27521653946472839 978770943064293241	10947872940354207279827244621638656461221656389407 6647	54	176.193
8761	192743 21086064775471 252738375533197927 978770943064293241	10053711262667729356732173297269613087936347577484 12871	55	179.392
8761	21086064775471 741360813207419388145717037710039122529073	15632382129287501672052151127791635330193623525414 768383	56	183.351
8761	192743 27521653946472839 252738375533197927 978770943064293241	13122162205001440555365121554393355974364591755440 75049439	58	189.742
8761	27521653946472839 741360813207419388145717037710039122529073	20403475750570287025793661909963361718760416618829 582348247	59	193.701
8761	252738375533197927 741360813207419388145717037710039122529073	18737032761401376286467302609955370744999748749777 5720831671	60	196.900
8761	978770943064293241 741360813207419388145717037710039122529073	72562242229393721856336708412074668114797095855002 9219895593	60	198.853
8761	192743 21086064775471 741360813207419388145717037710039122529073	30130322287452609347763477648239431684475095791590 18702444569	61	200.907
8761	192743 27521653946472839 741360813207419388145717037710039122529073	39326271265921688322125477775120682277590389803630 70190548171521	64	211.257
8761	192743 252738375533197927 741360813207419388145717037710039122529073	36114319055307854695825673069506280235034865732783 785760258763553	65	214.456
8761	192743 978770943064293241 741360813207419388145717037710039122529073	13985864254020034131755906189468507756450336646380 8281930336281599	66	216.409
8761	21086064775471 27521653946472839 252738375533197927 978770943064293241	14355632227831762653756380536427468813767778434785 1982337170951783	66	216.447
8761	192743 21086064775471 27521653946472839 252738375533197927 978770943064293241	27669476224889774291729660537326396215720429188558 034631613340759510769	71	234.003
8761	21086064775471 27521653946472839 741360813207419388145717037710039122529073	43022901132127685249474585600708647783813022090016 3214308801582985449337	72	237.962
8761	21086064775471 252738375533197927 741360813207419388145717037710039122529073	39509028650703168258121854698397160691749368911743 00334490383942000742041	73	241.161
8761	21086064775471 978770943064293241 741360813207419388145717037710039122529073	15300521399024132441310935207816284336673258678625 450530338256497607399303	74	243.114
8761	27521653946472839 252738375533197927 741360813207419388145717037710039122529073	51567413164301306399815193063717124104680398249601 94195440913352986092483969	76	251.511
8761	27521653946472839 978770943064293241 741360813207419388145717037710039122529073	19970329202175118203685799142226545766371028481239 139558224686062766190298527	77	253.464
8761	192743 21086064775471 27521653946472839 741360813207419388145717037710039122529073	82923630329096864380394800524373868997954733166960 158415521343509364461561391	77	255.518
8761	252738375533197927 978770943064293241 741360813207419388145717037710039122529073	18339263226103383632357114097529906737319806269135 4836594008350319132344035711	78	256.663
8761	192743 21086064775471 252738375533197927 741360813207419388145717037710039122529073	76150887092224807595751806401331639432098486121560 8169370680072133049023208463	78	258.717
8761	192743 21086064775471 978770943064293241 741360813207419388145717037710039122529073	29490683960121083591355935847601340919034138974943 05211568986572118342963858129	79	260.671
8761	192743 27521653946472839 252738375533197927 741360813207419388145717037710039122529073	99392579155269266994195797566800296513084139998230 2709811867962394598423637636967	81	269.067
8761	192743 27521653946472839 978770943064293241 741360813207419388145717037710039122529073	38491411614148388079330119840701711106476511425594 75475870900665795743816708989561	82	271.021
8761	192743 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	35347646119888444714514072425002068142712314197319 805269638951465560525386475045273	83	274.220
8761	21086064775471 27521653946472839 252738375533197927 741360813207419388145717037710039122529073	10873538142859333159640111242849829370810155236172 0763359202360112279855980367432651924399	90	295.772
8761	21086064775471 27521653946472839 978770943064293241 741360813207419388145717037710039122529073	42109565514454463839042488513456439315019022629473 9123404654249055451431450279784717031217	90	297.726
8761	21086064775471 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	38670289232002921109805158748342148170277093095471 95204458428579755894461134898393220844881	91	300.925
8761	27521653946472839 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	50472685614209239723398048029679629208293157524267 56817398592644097773349883203426487107553529	94	311.275
8761	192743 21086064775471 27521653946472839 252738375533197927 741360813207419388145717037710039122529073	20957983622691364511885139612806046624180617506855 145092142740495121156281223960071629864436457	95	313.329
8761	192743 21086064775471 27521653946472839 978770943064293241 741360813207419388145717037710039122529073	81163239859524967237285663635491344828947114786726 902862383273925694875252021276545714747858231	95	315.282
8761	192743 21086064775471 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	74534275574439390234671757126317106647837177545005 5045292930899747890366122523721004565304898583	96	318.481
8761	192743 27521653946472839 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	97282568433395314920069099713845407724940480606999 0389255856942001337128776538278031404571189840047	99	328.831
8761	21086064775471 27521653946472839 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	10642703182531993241353668757721062646060305921030 90654142325739482789074242760173832040893899797014 98687159	108	355.536
8761	192743 21086064775471 27521653946472839 252738375533197927 978770943064293241 741360813207419388145717037710039122529073	20513065395107639733182301773694307775896015441372 60019513542900051312145367723241849090580129285760 5961459087137	113	373.092

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-08-27	Seth_Tr	Manual testing	100000000	100000000		-	skipped known factor: 192743 skipped known factor: 21086064775471 skipped known factor: 252738375533197927 skipped known factor: 978770943064293241	-	-	0.018	-	-	5.594%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 192743 skipped known factor: 21086064775471 skipped known factor: 252738375533197927 skipped known factor: 978770943064293241	-	-	0.071	-	-	7.538%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2005-03-20	ANONYMOUS	v4_computers	?	?	192743 27521653946472839	72.168	22	6,806	2.31664e-6	14,758

ECM factoring results:

Total ECM effort:	3,117.511 GHz-days
Estimated T-Level:	46.509

Digits	B1	Complete	FacMiss
20	11000	5,583.800	0.000%
25	50000	1,577.692	0.000%
30	250000	425.253	0.000%
35	1000000	87.931	0.000%
40	3000000	15.253	0.000%
45	11000000	2.290	10.122%
50	44000000	0.302	73.942%
55	110000000	0.036	96.490%
60	260000000	0.004	99.627%

ECM Summary

B1	B2	factor	curves	GHz-days
3000000	300000000		3,217	24.56
3000000	300000000	741360813207419388145717037710039122529073	702	5.358
11000000	36578884662		9,600	3,088

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.008
2011-04-27	James Hintz	17_051310	3000000	300000000						11	0.084
2013-04-18	Axon		3000000	300000000						30	0.229
2018-06-05	James Hintz	3_1_2018	3000000	300000000	741360813207419388145717037710039122529073	139.089	702	2		702	5.358
2018-06-08	James Hintz	3_1_2018	3000000	300000000						3175	24.24
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9
2021-05-23	Bruno Victal	Manual testing	11000000	36578884662						2400	771.9

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

75966DB2719532__

2017-09-21

Oliver Kruse

Manual testing

75966DB2719532__

2017-10-02

kkmrkkblmbrbk

Manual testing

192743

21086064775471

27521653946472839

252738375533197927

978770943064293241

75966DB2719532__

2017-12-07

ATH

Manual testing

192743

21086064775471

27521653946472839

252738375533197927

978770943064293241

75966DB2719532__

2018-06-05

ATH

ec2-PRPCF

192743

21086064775471

27521653946472839

252738375533197927

978770943064293241

741360813207419388145717037710039122529073

0AF394F4D3633C__

2018-06-05

kkmrkkblmbrbk

c5.large

192743

21086064775471

27521653946472839

252738375533197927

978770943064293241

741360813207419388145717037710039122529073

0AF394F4D3633C__

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 = 400000000 (P-1 stage 1)

B1 = 100000000 (P-1 stage 1)

10⁰

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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