M3 340 531 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁹	35.7389	68.1159%	3340531	3357069870	28.3353	11.7716%	64.0741	71.8692%
Target	2⁶⁴	1.0655	65.6250%	18000	1500000	0.0150	1.7545%	1.0805	66.2281%
Difference	+5	+34.6734	+2.4909%	+3322531	+3355569870	+28.3202	+10.0172%	+62.9936	+5.6411%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
3340531	140302303	9	27.064	21 3 × 7	-	3	7	5.377e-12	4.901e-7	9.298e-7
3340531	835132751	9	29.637	125 5³	2008-09-07	125	125	2.199e-11	1.904e-5	3.874e-5
3340531	2349014631767	13	41.095	351593 11 × 31963	2008-09-30	11	31963	9.667e-8	0.0003	0.0005
3340531	331230311126703267943	21	68.166	49577493986241 3 × 13 × 379 × 8707 × 385223	2019-12-08	8707	385223	24.664	0.0045	0.0060

exponent	prime factors	composite factor	digits	bits*
3340531	140302303 835132751	117171048276025553	18	56.701
3340531	140302303 2349014631767	329572162617607059401	21	68.159
3340531	835132751 2349014631767	1961739051566826701017	22	70.733
3340531	140302303 331230311126703267943	46472375474482993290028972729	29	95.230
3340531	140302303 835132751 2349014631767	275236506819861544554577542151	30	97.797
3340531	835132751 331230311126703267943	276621280945829609717927701193	30	97.804
3340531	2349014631767 331230311126703267943	778064847321361719827801680545281	33	109.262
3340531	140302303 835132751 331230311126703267943	38810602775509912489016436864873747479	38	124.868
3340531	140302303 2349014631767 331230311126703267943	109164289962530430387881339207773220082143	42	136.326
3340531	835132751 2349014631767 331230311126703267943	649787436399883794145883263756203701598031	42	138.899
3340531	140302303 835132751 2349014631767 331230311126703267943	91166673787369725251045339874151809871328529565393	50	165.963

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2019-12-08	Jocelyn Larouche	Manual testing	50000	400000			331230311126703267943	21	68.166	0.011	0.702	0.021	1.235%
2020-05-01	Jocelyn Larouche	Manual testing	334053	3340531	6	-	skipped known factor: 140302303 skipped known factor: 835132751 skipped known factor: 2349014631767 skipped known factor: 331230311126703267943	-	-	0.076	-	-	3.092%
2020-07-05	Jocelyn Larouche	Manual testing	334053	6681062	6	-	skipped known factor: 140302303 skipped known factor: 835132751 skipped known factor: 2349014631767 skipped known factor: 331230311126703267943	-	-	0.104	-	-	3.618%
2021-08-03	Jocelyn Larouche	Manual testing	3340531	3340531		-	skipped known factor: 140302303 skipped known factor: 835132751 skipped known factor: 2349014631767 skipped known factor: 331230311126703267943	-	-	0.509	-	-	3.517%
2022-07-24	Jocelyn Larouche	Manual testing	3340531	3357069870		-	skipped known factor: 140302303 skipped known factor: 835132751 skipped known factor: 2349014631767 skipped known factor: 331230311126703267943	-	-	28.34	-	-	11.772%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07	Will Edgington	Manual testing	?	?	835132751	29.637	9	5.79277e-13	1.772	2.92616e-12
2008-09-30	markr	Manual testing	?	?	2349014631767	41.095	13	8.97836e-9	1.772	4.53533e-8
2021-01-30	Jocelyn Larouche	Manual testing	2⁶⁵	2⁶⁶		-	-	2.237	-	-
2021-02-01	Jocelyn Larouche	Manual testing	2⁶⁶	2⁶⁷		-	-	4.474	-	-
2021-02-02	Jocelyn Larouche	Manual testing	2⁶⁷	2⁶⁸		-	-	8.948	-	-
2021-08-23	Jocelyn Larouche	Manual testing	2⁶⁸	2⁶⁹	skipped known factors(?)	-	-	17.90	-	-

ECM factoring results:

Total ECM effort:	0.438 GHz-days
Estimated T-Level:	0.577

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.438

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2018-10-04	Oliver Kruse	ECM-HTC	50000	5000000						3	0.438

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-11-04

Oliver Kruse

GTX-0

140302303

835132751

2349014631767

54F4F040C4CABF__

2017-12-15

kkmrkkblmbrbk

c4.xlarge

140302303

835132751

2349014631767

54F4F040C4CABF__

2019-12-09

Niels_Mache_Nextcloud

SuperDry-X

140302303

835132751

2349014631767

331230311126703267943

54F4F040C4CABFDB

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 = 3340531, B2 = 3357069870 (P-1 stage 2)

B1 = 3340531 (P-1 stage 1)

B1 = 334053, B2 = 6681062 (P-1 stage 2)

B1 = 334053, B2 = 3340531 (P-1 stage 2)

B1 = 334053 (P-1 stage 1)

B1 = 50000, B2 = 400000 (P-1 stage 2)

B1 = 50000 (P-1 stage 1)

10⁰

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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