M640 421 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	unknown	1750000	7199692500	8.6787	46.6382%	8.6787	46.6382%
Target	2⁴⁴	0.0000	54.5455%	11000	400000	0.0007	15.9307%	0.0007	61.7867%
Difference	-44	0.0000	-54.5455%	+1739000	+7199292500	+8.6780	+30.7075%	+8.6780	-15.1485%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
640421	24335999	8	24.537	19 19	-	1	19	3.504e-12	4.364e-8	4.484e-8
640421	62232801161728159	17	55.789	48587414499 3² × 13 × 17807 × 23321	2014-10-14	17807	23321	0.0104	0.0004	0.0008
640421	21077263836840832627337	23	74.158	16455787549784308 2² × 11 × 4637 × 4813 × 16757647	2014-10-14	4813	16757647	9,501.6	0.0202	0.0376
640421	232500634753928846430404432521	30	97.553	181521713649247015971060 2² × 3² × 5 × 17 × 233 × 19577 × 121789 × 106781749	2023-01-24	121789	106781749	8.331e+10	0.1307	0.2394

exponent	prime factors	composite factor	digits	bits*
640421	24335999 62232801161728159	1514497386839015315695841	25	80.325
640421	24335999 21077263836840832627337	512936271656094665978040604663	30	98.695
640421	24335999 232500634753928846430404432521	5658135214870977652801475839426623479	37	122.090
640421	62232801161728159 21077263836840832627337	1311697169391399082660914917783346082583	40	129.947
640421	62232801161728159 232500634753928846430404432521	14469165772616837493147249748780351818061058839	47	153.342
640421	24335999 62232801161728159 21077263836840832627337	31921461002611918684236942778260592482393805417	47	154.483
640421	21077263836840832627337 232500634753928846430404432521	49004772209415233533624272408562061634721229564265 77	52	171.711
640421	24335999 62232801161728159 232500634753928846430404432521	35212160377323758461639397673906889306398210984484 5161	54	177.878
640421	24335999 21077263836840832627337 232500634753928846430404432521	11925800874835569138590467597104939233805142079547 4221445423	60	196.248
640421	62232801161728159 21077263836840832627337 232500634753928846430404432521	30497042448843201465096543395199516522145790353762 6331116684516881743	69	227.500
640421	24335999 62232801161728159 21077263836840832627337 232500634753928846430404432521	74217599453800570201138801496903203888342343190337 70856429303286149580766257	76	252.036

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2014-10-14	alpertron	Manual testing	1000000	30000000	12		62232801161728159 21077263836840832627337	40	129.947	0.057	0.019	0.114	31.591%
2023-01-24	USAFSS	USAFSACS	1750000	7199692500			232500634753928846430404432521	30	97.553	8.679	0.019	17.36	46.638%

ECM factoring results:

Total ECM effort:	18.833 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	4.785
250000	25000000	44	3.746
250000	40000000	100	10.30

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2014-12-26	Richard B. Woods	Puttputt	50000	5000000						1	0.017
2015-09-11	TJAOI	Manual testing	50000	5000000						99	1.686
2016-04-22	TJAOI	Manual testing	50000	5000000						90	1.533
2016-09-30	TJAOI	Manual testing	50000	5000000						91	1.550
2019-03-01	TJAOI	Manual testing	250000	25000000						44	3.746
2023-01-15	TJAOI	Manual testing	250000	40000000						100	10.30

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

24335999

62232801161728159

21077263836840832627337

68A3CD2F8BB397CC

2017-09-28

Oliver Kruse

Manual testing

24335999

62232801161728159

21077263836840832627337

68A3CD2F8BB397__

2017-10-13

Oliver Kruse

Threadripper

68A3CD2F8BB397__

2017-12-16

ATH

ec2-1xf

24335999

62232801161728159

21077263836840832627337

68A3CD2F8BB397__

2020-04-19

Oliver Kruse

AddPrpType5

24335999

62232801161728159

21077263836840832627337

1A090F074A954A__

2023-01-24

LordJulius

WhiteBox

24335999

62232801161728159

21077263836840832627337

232500634753928846430404432521

1A090F074A954ADB

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 = 7199692500 (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