M725 111 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	1500000	3613488450	5.7425	45.1205%	5.7425	45.1205%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5665%	0.0010	62.0757%
Difference	-44	0.0000	-54.5455%	+1488000	+3613038450	+5.7414	+28.5540%	+5.7414	-16.9552%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
725111	935393191	9	29.801	645 3 × 5 × 43	-	5	43	1.124e-10	2.048e-7	2.947e-7
725111	2834577416080246171273	22	71.264	1954581723405276 2² × 3 × 7 × 17 × 151 × 619 × 14643943	2014-10-08	619	14643943	1,127.0	0.0231	0.0432
725111	9038250838445443311406657	25	82.902	6232322250279918048 2⁵ × 3 × 4177 × 490499 × 31686631	2023-01-04	490499	31686631	1,785,839	0.0634	0.0934

exponent	prime factors	composite factor	digits	bits*
725111	935393191 2834577416080246171273	2651444414363836178212584002143	31	101.065
725111	935393191 9038250838445443311406657	8454318292831908698466279589872487	34	112.703
725111	2834577416080246171273 9038250838445443311406657	25619621707525803183411794021291862872174364361	47	154.166
725111	935393191 2834577416080246171273 9038250838445443311406657	23964419701215429754569516276610917554337603788032 465951	56	183.967

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2014-10-08	alpertron	Manual testing	500000	15000000	12		2834577416080246171273	22	71.264	0.037	0.029	0.075	29.491%
2023-01-04	USAFSS	6917th_Scty_Sq	1500000	3613488450			9038250838445443311406657	25	82.902	5.742	0.029	11.48	45.120%

ECM factoring results:

Total ECM effort:	11.336 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	6.358
250000	25000000		44	4.978

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-09	TJAOI	Manual testing	50000	5000000						100	2.263
2016-06-17	TJAOI	Manual testing	50000	5000000						90	2.036
2017-09-01	TJAOI	Manual testing	50000	5000000						91	2.059
2018-11-02	TJAOI	Manual testing	250000	25000000						44	4.978

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-3

935393191

2834577416080246171273

CD5F6C97CE2EDD__

2017-09-28

Oliver Kruse

Manual testing

935393191

2834577416080246171273

CD5F6C97CE2EDD__

2017-11-09

kkmrkkblmbrbk

c4.large

935393191

2834577416080246171273

CD5F6C97CE2EDD__

2020-04-20

Oliver Kruse

AddPrpType5

935393191

2834577416080246171273

0BE75D11098327__

2023-01-06

LordJulius

WhiteBox

935393191

2834577416080246171273

9038250838445443311406657

0BE75D11098327B2

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 = 1500000, B2 = 3613488450 (P-1 stage 2)

B1 = 1500000 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (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