M617 531 Mersenne number exponent details

≡

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	unknown	1750000	5399784390	6.5181	45.8782%	6.5181	45.8782%
Target	2⁴⁴	0.0000	54.5455%	10000	360000	0.0006	15.4812%	0.0006	61.5824%
Difference	-44	0.0000	-54.5455%	+1740000	+5399424390	+6.5175	+30.3970%	+6.5175	-15.7041%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
617531	1235063	7	20.236	1 1	-	1	1	2.263e-13	2.203e-8	4.484e-8
617531	850356361338119526738856303	27	89.458	688513095972606660021 3² × 7 × 61 × 373 × 2861 × 3209 × 52317311	2023-01-07	3209	52317311	333,139,026	0.0629	0.1173

exponent	prime factors	composite factor	digits	bits*
617531	1235063 850356361338119526738856303	1050243678703341917052672082152089	34	109.694

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-17	alpertron	Manual testing	1000000	30000000	12	-	skipped known factor: 1235063	-	-	0.057	-	-	31.516%
2023-01-07	USAFSS	USAFSACS	1750000	5399784390			850356361338119526738856303	27	89.458	6.518	0.019	13.04	45.878%

ECM factoring results:

Total ECM effort:	8.507 GHz-days
Estimated T-Level:	25.658

Digits	B1	Complete	FacMiss
20	11000	14.808	0.000%
25	50000	1.620	19.795%
30	250000	0.132	87.678%
35	1000000	0.009	99.129%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		281	4.771
250000	25000000		44	3.735

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-12-30	Richard B. Woods	Puttputt	50000	5000000						1	0.017
2015-09-04	TJAOI	Manual testing	50000	5000000						99	1.681
2016-05-06	TJAOI	Manual testing	50000	5000000						90	1.528
2016-12-02	TJAOI	Manual testing	50000	5000000						91	1.545
2018-11-09	TJAOI	Manual testing	250000	25000000						44	3.735

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-0

1235063

D57E4CE16EFC45__

2017-10-13

Oliver Kruse

Threadripper

D57E4CE16EFC45__

2017-12-15

ATH

ec2-1xf

1235063

D57E4CE16EFC45__

2020-04-19

Oliver Kruse

AddPrpType5

1235063

E37126071FDFDF__

2022-05-12

Jorge Coveiro

Manual testing

1235063

E37126071FDFDF6D

2023-01-08

LordJulius

WhiteBox

1235063

850356361338119526738856303

E37126071FDFDF6D

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 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1750000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

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