M2 787 859 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	10.6583	67.1642%	330000	261254070	1.6290	7.7931%	12.2874	69.7231%
Target	2⁶³	0.5725	65.0794%	15000	240000	0.0031	1.7484%	0.5755	65.6899%
Difference	+4	+10.0858	+2.0848%	+315000	+261014070	+1.6260	+6.0447%	+11.7118	+4.0332%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2787859	646783289	9	29.269	116 2² × 29	-	4	29	2.630e-11	6.005e-7	9.117e-7
2787859	6222501289	10	32.535	1116 2² × 3² × 31	2008-09-07	9	31	2.548e-10	1.142e-6	2.051e-6
2787859	20100257112432135603593	23	74.090	3604963004304044 2² × 1193 × 9157 × 82498711	2023-01-19	9157	82498711	2,240.9	0.5043	0.9402

exponent	prime factors	composite factor	digits	bits*
2787859	646783289 6222501289	4024609849506159521	19	61.804
2787859	646783289 20100257112432135603593	13000510404924499454985880757377	32	103.358
2787859	6222501289 20100257112432135603593	125073875791340381718380235531377	33	106.624
2787859	646783289 6222501289 20100257112432135603593	80895692752300609806329440489578678758953	41	135.893

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2023-01-19	USAFSS	USAFSACS	330000	261254070			20100257112432135603593	23	74.090	1.629	0.431	3.258	7.793%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07	Will Edgington	Manual testing	?	?	6222501289	32.535	10	4.95764e-11	1.006	2.31666e-10

ECM factoring results:

Total ECM effort:	0.312 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.312

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-04-26	ATH	ec2-ECMCF	50000	5000000						3	0.312

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-21

Oliver Kruse

GTX-1

646783289

6222501289

19D3DF5F10C931__

2017-12-06

kkmrkkblmbrbk

c4.xlarge

646783289

6222501289

19D3DF5F10C931__

2023-01-22

LordJulius

WhiteBox

646783289

6222501289

20100257112432135603593

19D3DF5F10C93188

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 = 330000, B2 = 261254070 (P-1 stage 2)

B1 = 330000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

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