M725 749 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	40.9424	70.1493%	1500000	3613488450	5.7425	11.1047%	46.6849	73.4641%
Target	2⁴⁴	0.0000	54.5455%	12000	450000	0.0010	16.5682%	0.0010	62.0764%
Difference	+23	+40.9424	+15.6038%	+1488000	+3613038450	+5.7414	-5.4634%	+46.6838	+11.3877%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
725749	13986634729	11	33.703	9636 2² × 3 × 11 × 73	-	11	73	1.712e-9	4.164e-7	6.483e-7
725749	1376494743847	13	40.324	948327 3 × 316109	2008-07-16	3	316109	2.554e-7	0.0005	0.0009
725749	390181525656045793052248423687	30	98.300	268812995716181347168407 3 × 6451 × 112111 × 260419 × 475752491	2023-01-05	260419	475752491	1.027e+11	0.7578	1.4020

exponent	prime factors	composite factor	digits	bits*
725749	13986634729 1376494743847	19252529188576409262463	23	74.027
725749	13986634729 390181525656045793052248423687	5457326477355054597918924714276100425823	40	132.003
725749	1376494743847 390181525656045793052248423687	537082819211750412534356666250446592303889	42	138.624
725749	13986634729 1376494743847 390181525656045793052248423687	75119812115362967248331098538511585196772780091610 81	52	172.328

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	500000	15000000	12	-	skipped known factor: 13986634729 skipped known factor: 1376494743847	-	-	0.037	-	-	4.529%
2023-01-05	USAFSS	6917th_Scty_Sq	1500000	3613488450			390181525656045793052248423687	30	98.300	5.742	0.029	11.48	11.105%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-07-16	J Feitsma	Manual testing	?	?	1376494743847	40.324	13	5.36018e-8	0.030	1.11055e-7

ECM factoring results:

Total ECM effort:	11.337 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	6.359
250000	25000000		44	4.978

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-10-23	TJAOI	Manual testing	50000	5000000						100	2.263
2016-06-24	TJAOI	Manual testing	50000	5000000						90	2.037
2017-09-29	TJAOI	Manual testing	50000	5000000						91	2.059
2018-11-30	TJAOI	Manual testing	250000	25000000						44	4.978

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27

Oliver Kruse

GTX-1

13986634729

1376494743847

F06D7A40928C14__

2017-09-28

Oliver Kruse

Manual testing

13986634729

1376494743847

F06D7A40928C14__

2017-11-09

kkmrkkblmbrbk

c4.large

13986634729

1376494743847

F06D7A40928C14__

2020-04-20

Oliver Kruse

AddPrpType5

13986634729

1376494743847

0159D61B3A1A63__

2023-01-06

LordJulius

WhiteBox

13986634729

1376494743847

390181525656045793052248423687

0159D61B3A1A637C

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