M1388659 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	21.3976	68.6567%	500000	15000000	0.0714	4.9024%	21.4690	70.1933%	1.5366%
PrimeNet	2⁵⁶	0.0069	62.5000%	6500	110000	0.0007	2.7578%	0.0076	63.5342%	1.0342%
GPU72	2⁶⁰	0.1106	65.0000%	5500	70000	0.0005	1.2015%	0.1111	65.4205%	0.4205%
Difference	+7	+21.2870	+3.6567%	+494500	+14930000	+0.0709	+3.7010%	+21.3579	+4.7728%	+4.7728%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1388659	25262484529	11	34.556	9096 2³ × 3 × 379	-	8	379	3.245e-9	1.562e-6	2.138e-6
1388659	10725924351097	14	43.286	3861972 2² × 3³ × 35759	2008-07-15	27	35759	1.624e-6	0.0001	0.0002
1388659	157185236737951997209	21	67.091	56596053004356 2² × 3 × 353 × 839 × 15924589	2015-01-18	839	15924589	21.845	0.0481	0.0897
1388659	348250303198755524849	21	68.239	125390863847336 2³ × 3823 × 4099884379	2018-08-09	3823	4099884379	70.281	12.367	23.097
1388659	401697676255545113761	21	68.445	144635103454320 2⁴ × 3² × 5 × 239 × 3691 × 227719	2015-01-18	3691	227719	85.414	0.0009	0.0013

exponent	prime factors	composite factor	digits	bits*
1388659	25262484529 10725924351097	270963497978812326678313	24	77.842
1388659	25262484529 157185236737951997209	3970889611279714756637013679561	31	101.647
1388659	25262484529 348250303198755524849	8797667896778120658551137561121	31	102.795
1388659	25262484529 401697676255545113761	10147881331740959086848807503569	32	103.0009
1388659	10725924351097 157185236737951997209	1685956958360546100696678480088273	34	110.377
1388659	10725924351097 348250303198755524849	3735306407356445356283953983909353	34	111.525
1388659	10725924351097 401697676255545113761	4308578887528430509064962970145817	34	111.731
1388659	157185236737951997209 348250303198755524849	54739806352359948853855370209642578146441	41	135.330
1388659	157185236737951997209 401697676255545113761	63140944339313057482163445956931059493049	41	135.536
1388659	348250303198755524849 401697676255545113761	139891337550229123772232273715164967347089	42	136.683
1388659	25262484529 10725924351097 157185236737951997209	42591461577143193072841116224917231216828417	44	144.933
1388659	25262484529 10725924351097 348250303198755524849	94363120326916772601557280449457945100899737	44	146.081
1388659	25262484529 10725924351097 401697676255545113761	108845407488163006782905221289266590836565193	45	146.287
1388659	25262484529 157185236737951997209 348250303198755524849	13828635110969491305597525719246631170441392589112 89	52	169.886
1388659	25262484529 157185236737951997209 401697676255545113761	15950971295183462411308417469362984907627289455389 21	52	170.092
1388659	25262484529 348250303198755524849 401697676255545113761	35340027506037799997012439345238483402886260356860 81	52	171.240
1388659	10725924351097 157185236737951997209 348250303198755524849	58713502192911182294486077060254927485766729596499 5777	54	178.616
1388659	10725924351097 157185236737951997209 401697676255545113761	67724499244029820146111301972728920250254629710702 4753	54	178.822
1388659	10725924351097 348250303198755524849 401697676255545113761	15004639039375327040403513472754916918006327758969 06633	55	179.970
1388659	157185236737951997209 348250303198755524849 401697676255545113761	21988853010421518611641499434011668575737620422697 597862274601	62	203.774
1388659	25262484529 10725924351097 157185236737951997209 348250303198755524849	14832489407918263161855532437405919064051988741344 969942012834033	65	213.172
1388659	25262484529 10725924351097 157185236737951997209 401697676255545113761	17108891143865755270557892855981115277329323913772 450279882546337	65	213.378
1388659	25262484529 10725924351097 348250303198755524849 401697676255545113761	37905446159544862118250911702271415164981521653505 927915119980857	65	214.526
1388659	25262484529 157185236737951997209 348250303198755524849 401697676255545113761	55549305898622868969527893874608203380004710069167 2506441175580512147929	72	238.331
1388659	10725924351097 157185236737951997209 348250303198755524849 401697676255545113761	23585077395717274199301615816674769903974476253045 3627201178354107349587297	75	247.061
1388659	25262484529 10725924351097 157185236737951997209 348250303198755524849 401697676255545113761	59581765282457525031790793217344807492379002195343 63648521701741206602554284997428113	85	281.617

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2015-01-19T11:24:00	alpertron	Manual testing	500000	15000000	12		157185236737951997209 401697676255545113761	41	135.536	0.071	0.106	0.143	4.902%

	Bits	Factor	GHz-Days	worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved
2008-07-15T09:59:00	J Feitsma	Manual testing	?	?	10725924351097	43.286	14	7.80274e-7	0.115	1.68801e-6

ECM factoring results:

Old Calculation Method

Total ECM effort:	25.329 GHz-days
Estimated T-Level:	25.391

Digits	B1	Curves	Complete	FacMiss
20	11000	301 / 100	3.010	4.855%
25	50000	301 / 280	1.075	34.064%
30	250000	50 / 640	0.078	92.479%

New Calculation Method

Total ECM effort:	25.329 GHz-days
Estimated T-Level:	25.391

Digits	B1	Complete	FacMiss
20	11000	12.263	0.000%
25	50000	1.357	25.749%
30	250000	0.113	89.315%
35	1000000	0.008	99.236%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		249	11.70
50000	5000000	348250303198755524849	2	0.094
250000	35000000		50	13.54

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-11-14T16:14:15	storm5510	7700_Kaby_Lake	50000	5000000						3	0.141
2018-08-09T15:06:29	Chang Chia-Tche	exbpc13	50000	5000000	348250303198755524849	68.239	2	2		2	0.094
2018-12-14T12:20:24	TJAOI	Manual testing	50000	5000000						246	11.56
2021-09-03T08:15:28	TJAOI	Manual testing	250000	35000000						50	13.54

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T13:34:27

Oliver Kruse

GTX-3

25262484529

10725924351097

157185236737951997209

401697676255545113761

1250AE90CF3D05C5

2017-10-05T21:42:16

Oliver Kruse

Manual testing

25262484529

10725924351097

157185236737951997209

401697676255545113761

1250AE90CF3D05__

2017-10-25T09:11:11

Chang Chia-Tche

homura

25262484529

10725924351097

157185236737951997209

401697676255545113761

1250AE90CF3D05__

2018-08-09T15:17:29

ATH

ec2-PRPCF

25262484529

10725924351097

157185236737951997209

348250303198755524849

401697676255545113761

C3518CDB4824DB__

2018-08-12T07:18:16

Oliver Kruse

GTX-1

25262484529

10725924351097

157185236737951997209

348250303198755524849

401697676255545113761

C3518CDB4824DB__

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