M8 081 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	73000000000	299074993103236350	2,402,080.8280	80.1578%	2,402,080.8280	80.1578%
Target	2⁴⁴	0.0003	70.4545%	500	10000	0.0000	1.1834%	0.0003	70.8042%
Difference	-44	-0.0003	-70.4545%	+72999999500	+299074993103226350	+2,402,080.8280	+78.9744%	+2,402,080.8278	+9.3536%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
8081	3498814409	10	31.704	216484 2² × 54121	-	4	54121	6.578e-8	4.352e-7	8.119e-7
8081	36263568311	11	35.078	2243755 5 × 53 × 8467	-	53	8467	9.410e-7	7.539e-8	1.270e-7
8081	56994371767	11	35.730	3526443 3³ × 211 × 619	-	211	619	7.360e-7	3.438e-8	6.330e-8
8081	272050792367	12	37.985	16832743 37 × 281 × 1619	-	281	1619	3.287e-6	5.217e-8	8.431e-8
8081	1343743045821830104657	22	70.187	83142126334725288 2³ × 3 × 22273 × 322513 × 482263	-	322513	482263	45,249	4.883e-5	9.676e-5

exponent	prime factors	composite factor	digits	bits*
8081	3498814409 36263568311	126879495328282593199	21	66.782
8081	3498814409 56994371767	199412729170282390703	21	67.434
8081	3498814409 272050792367	951855232313526816103	21	69.689
8081	36263568311 56994371767	2066819293915134275537	22	70.808
8081	36263568311 272050792367	9865532493062381882137	22	73.063
8081	56994371767 272050792367	15505363999671723902489	23	73.715
8081	3498814409 1343743045821830104657	4701507530714966416923889602713	31	101.891
8081	3498814409 36263568311 56994371767	7231417126349477826418631812633	31	102.512
8081	3498814409 36263568311 272050792367	34517667239184354265081475312033	32	104.767
8081	36263568311 1343743045821830104657	48728917734591139135265398724327	32	105.265
8081	3498814409 56994371767 272050792367	54250390978841298859898224164001	32	105.419
8081	56994371767 1343743045821830104657	76585790712890301029133576018919	32	105.917
8081	272050792367 1343743045821830104657	365566360353474868677991386753119	33	108.172
8081	36263568311 56994371767 272050792367	562279826589015741313041354426079	33	108.793
8081	3498814409 36263568311 1343743045821830104657	170493439504763115330190377095805526427743	42	136.969
8081	3498814409 56994371767 1343743045821830104657	267959468070918967277080084560690653803871	42	137.621
8081	3498814409 272050792367 1343743045821830104657	1279048849050424203749939045149704482891671	43	139.876
8081	3498814409 36263568311 56994371767 272050792367	1967312759159669596833885670478841130572311	43	140.497
8081	36263568311 56994371767 1343743045821830104657	2777274053168846819619339035105780584875809	43	140.995
8081	36263568311 272050792367 1343743045821830104657	13256740680881878006526094915791351348812009	44	143.250
8081	56994371767 272050792367 1343743045821830104657	20835225047495036195724944907431143332791273	44	143.902
8081	3498814409 36263568311 56994371767 1343743045821830104657	97171664749689933623979673110842619495559280047318 81	52	172.699
8081	3498814409 36263568311 272050792367 1343743045821830104657	46382875310645985596213696925872421736805042121437 681	53	174.954
8081	3498814409 56994371767 272050792367 1343743045821830104657	72898585610933341997578981442851255468114388161852 657	53	175.606
8081	36263568311 56994371767 272050792367 1343743045821830104657	75555960678489446451708910581734083777750853474014 9903	54	178.980
8081	3498814409 36263568311 56994371767 272050792367 1343743045821830104657	26435628390773629159967305901706378452800783974693 13551436352327	64	210.684

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: 3498814409 skipped known factor: 36263568311 skipped known factor: 56994371767 skipped known factor: 272050792367 skipped known factor: 1343743045821830104657	-	-	0.015	-	-	26.197%
2021-08-27	Seth_Tr	Manual testing	400000000	400000000		-	skipped known factor: 3498814409 skipped known factor: 36263568311 skipped known factor: 56994371767 skipped known factor: 272050792367 skipped known factor: 1343743045821830104657	-	-	0.059	-	-	29.883%
2023-05-27	JacobZ	GreatLakes	73000000000	299074993103236350		-	skipped known factor: 3498814409 skipped known factor: 36263568311 skipped known factor: 56994371767 skipped known factor: 272050792367 skipped known factor: 1343743045821830104657	-	-	2,402,081	-	-	80.158%

ECM factoring results:

Total ECM effort:	1,300.704 GHz-days
Estimated T-Level:	44.256

Digits	B1	Complete	FacMiss
20	11000	2,425.050	0.000%
25	50000	676.951	0.000%
30	250000	173.130	0.000%
35	1000000	34.529	0.000%
40	3000000	5.807	0.301%
45	11000000	0.851	42.692%
50	44000000	0.110	89.583%
55	110000000	0.013	98.726%
60	260000000	0.001	99.872%

ECM Summary

B1	B2	curves	GHz-days
3000000	300000000	3,764	23.95
3000000	3000000000	89	2.224
11000000	36578884662	2,400	643.5
11000000	99324315090	900	631.0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.006
2013-04-18	Axon		3000000	300000000						30	0.191
2016-09-14	Adam Buran	fhas	3000000	3000000000						89	2.224
2017-05-28	kkmrkkblmbrbk	old	3000000	300000000						3733	23.76
2020-12-14	Bruno Victal	Manual testing	11000000	36578884662						2400	643.5
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2
2023-01-27	Denial140	i5-8400	11000000	99324315090						150	105.2

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

7023AB48E1D93B__

2017-09-21

Oliver Kruse

Manual testing

7023AB48E1D93B__

2017-10-02

kkmrkkblmbrbk

Manual testing

3498814409

36263568311

56994371767

272050792367

1343743045821830104657

7023AB48E1D93B__

2017-12-07

ATH

Manual testing

3498814409

36263568311

56994371767

272050792367

1343743045821830104657

7023AB48E1D93B__

2020-04-17

Oliver Kruse

Manual testing

3498814409

36263568311

56994371767

272050792367

1343743045821830104657

154003DB2731B8__

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 = 73000000000, B2 = 299074993103236350 (P-1 stage 2)

B1 = 73000000000 (P-1 stage 1)

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