M610 457 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	48.6749	70.1493%	1750000	5543237700	6.6903	11.6003%	55.3652	73.6120%
Target	2⁴⁴	0.0000	54.5455%	10000	360000	0.0006	15.4600%	0.0006	61.5727%
Difference	+23	+48.6749	+15.6038%	+1740000	+5542877700	+6.6897	-3.8597%	+55.3646	+12.0393%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
610457	90715237147939073	17	56.332	74301086848 2⁷ × 580477241	2001-10-20	128	580477241	0.0209	0.6968	1.3014
610457	82857241805669608225014032416903	32	106.030	67864928902174607077168443 3² × 107 × 11243 × 43633 × 134093 × 1071311383	2022-12-19	134093	1071311383	2.172e+11	1.2888	2.4018

exponent	prime factors	composite factor	digits	bits*
610457	90715237147939073 82857241805669608225014032416903	7516414339825449997896905264106789818759579350919	49	162.363

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2000-12-07	Alex Kruppa	v4_computers	100000	4000000		-		-	-	0.007	-	-	2.574%
2016-03-17	alpertron	Manual testing	1000000	30000000	12	-		-	-	0.057	-	-	5.472%
2022-12-19	USAFSS	6917th_Scty_Sq	1750000	5543237700			82857241805669608225014032416903	32	106.030	6.690	0.019	13.38	11.600%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-10-20	ANONYMOUS	v4_computers	?	?	90715237147939073	56.332	17	0.005	0.019	0.011
2003-08-25	ANONYMOUS	v4_computers	?	?	90715237147939073	56.332	17	0.005	0.019	0.011
2001-04-08	ANONYMOUS	v4_computers	2¹	2⁵⁶		-	-	0.016	-	-

ECM factoring results:

Total ECM effort:	18.754 GHz-days
Estimated T-Level:	26.530

Digits	B1	Complete	FacMiss
20	11000	24.808	0.000%
25	50000	3.182	4.149%
30	250000	0.306	73.637%
35	1000000	0.023	97.679%
40	3000000	0.002	99.849%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	4.767
250000	25000000	44	3.732
250000	40000000	100	10.26

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-12-08	Richard B. Woods	Puttputt	50000	5000000						1	0.017
2015-08-28	TJAOI	Manual testing	50000	5000000						99	1.679
2016-04-01	TJAOI	Manual testing	50000	5000000						90	1.527
2016-10-28	TJAOI	Manual testing	50000	5000000						91	1.544
2018-10-19	TJAOI	Manual testing	250000	25000000						44	3.732
2022-09-19	TJAOI	Manual testing	250000	40000000						100	10.26

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-0

90715237147939073

348C486DE9E0AB__

2017-10-13

Oliver Kruse

Threadripper

348C486DE9E0AB__

2017-12-16

ATH

ec2-1xf

90715237147939073

348C486DE9E0AB__

2020-04-19

Oliver Kruse

AddPrpType5

90715237147939073

17B215670928BA__

2022-12-19

LordJulius

WhiteBox

90715237147939073

82857241805669608225014032416903

17B215670928BAA4

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 = 5543237700 (P-1 stage 2)

B1 = 1000000, B2 = 30000000 (P-1 stage 2)

B1 = 1750000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

B1 = 100000, B2 = 4000000 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁵⁶

this exponent TF target: 44

TF double-checked to: 67.7

ECM T-Level=26.53 ~= 72-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

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