M582 851 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	50.9803	70.1493%	1750000	5399784390	6.2560	11.5229%	57.2363	73.5889%
Target	2⁴⁴	0.0000	54.5455%	10000	340000	0.0006	15.2372%	0.0006	61.4715%
Difference	+23	+50.9803	+15.6038%	+1740000	+5399444390	+6.2554	-3.7144%	+57.2357	+12.1174%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
582851	32639657	8	24.960	28 2² × 7	-	4	7	3.858e-12	8.804e-8	1.721e-7
582851	32873962103	11	34.936	28201 28201	2008-07-21	1	28201	4.336e-9	3.251e-5	6.068e-5
582851	4194750345845314830720553	25	81.795	3598475721792803676 2² × 3² × 11 × 353 × 5521 × 4662629837	2022-12-25	5521	4662629837	1,032,292	5.3718	10.033
582851	599592871185411307034905727	27	88.954	514362050665960345813 59 × 263 × 33148292238574489	2021-11-11	263	33148292238574489	137,185,016	38,189,595	71,327,528

exponent	prime factors	composite factor	digits	bits*
582851	32639657 32873962103	1072994847272918671	19	59.896
582851	32639657 4194750345845314830720553	136915212489022451131731912770321	33	106.755
582851	32639657 599592871185411307034905727	19570505655137008465541009956615639	35	113.914
582851	32873962103 4194750345845314830720553	137898063900865023245211319505202959	36	116.731
582851	32873962103 599592871185411307034905727	19710993324578171993933188167575663881	38	123.890
582851	32639657 32873962103 4194750345845314830720553	4500945506688316362020724361167234297145063	43	141.691
582851	32639657 32873962103 599592871185411307034905727	643360061243521203568985342706128190623128817	45	148.850
582851	4194750345845314830720553 599592871185411307034905727	25151424037713893855589180249732766272029538363070 31	52	170.749
582851	32639657 4194750345845314830720553 599592871185411307034905727	82093385365253655958083837626245183278021282603895 638528367	59	195.709
582851	32873962103 4194750345845314830720553 599592871185411307034905727	82682696065228978936520326626655103430405563304415 802566446193	62	205.685
582851	32639657 32873962103 4194750345845314830720553 599592871185411307034905727	26987348394043234989482482346219896332679609571479 18381148523448475801	70	230.645

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2022-12-25	USAFSS	USAFSACS	1750000	5399784390			4194750345845314830720553	25	81.795	6.256	0.017	12.51	11.523%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-21	J Feitsma	Manual testing	?	?	32873962103	34.936	11	4.08817e-10	0.018	8.46283e-10

ECM factoring results:

Total ECM effort:	17.367 GHz-days
Estimated T-Level:	26.502

Digits	B1	Complete	FacMiss
20	11000	24.808	0.000%
25	50000	3.135	4.351%
30	250000	0.300	74.050%
35	1000000	0.023	97.711%
40	3000000	0.001	99.851%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	4.559
250000	25000000		44	3.569
250000	35000000		24	2.217
250000	35000000	599592871185411307034905727	76	7.021

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-06-27	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-09-04	TJAOI	Manual testing	50000	5000000						100	1.622
2016-03-18	TJAOI	Manual testing	50000	5000000						89	1.444
2016-10-21	TJAOI	Manual testing	50000	5000000						91	1.476
2018-11-02	TJAOI	Manual testing	250000	25000000						44	3.569
2021-11-11	TJAOI	Manual testing	250000	35000000	599592871185411307034905727	88.954	76	2		76	7.021
2021-11-11	TJAOI	Manual testing	250000	35000000						24	2.217

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

32639657

32873962103

BAE2D90FD54186__

2017-09-28

Oliver Kruse

Manual testing

32639657

32873962103

BAE2D90FD54186__

2017-11-08

kkmrkkblmbrbk

c4.xlarge

32639657

32873962103

BAE2D90FD54186__

2020-04-19

Oliver Kruse

AddPrpType5

32639657

32873962103

6CF62FEDC9A7A8__

2021-11-11

SRJ2877

LTOS

32639657

32873962103

599592871185411307034905727

6CF62FEDC9A7A8FB

2022-12-26

LordJulius

WhiteBox

32639657

32873962103

4194750345845314830720553

599592871185411307034905727

6CF62FEDC9A7A8FB

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 = 1750000, B2 = 5399784390 (P-1 stage 2)

B1 = 1750000 (P-1 stage 1)

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10¹⁷

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