M534923 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	55.5480	70.1493%	2000000	6733146420	7.7971	11.8488%	63.3452	73.6862%	3.5370%
Target	2⁴⁴	0.0000	54.5455%	9000	300000	0.0005	14.6415%	0.0005	61.2007%	6.6552%
Difference	+23	+55.5480	+15.6038%	+1991000	+6732846420	+7.7966	-2.7927%	+63.3446	+12.4855%	-3.1183%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
534923	360538103	9	28.426	337 337	-	1	337	7.173e-11	4.082e-7	7.281e-7
534923	75518688565818607	17	56.068	70588373061 3 × 23529457687	2015-03-05	3	23529457687	0.0292	27.108	50.630
534923	550097583190851024327654398832916947049	39	128.693	514183894869776607406724331196188 2² × 3² × 2887 × 8849 × 14341 × 272449 × 1581637 × 90469777	2022-12-19	1581637	90469777	2.818e+11	0.1359	0.1947

exponent	prime factors	composite factor	digits	bits*
534923	360538103 75518688565818607	27227364716568031209882521	26	84.493
534923	360538103 550097583190851024327654398832916947049	198331139108514115266699367394825290045597908047	48	157.119
534923	75518688565818607 550097583190851024327654398832916947049	41542648065799371195794484046887142579169444437957 940743	56	184.761
534923	360538103 75518688565818607 550097583190851024327654398832916947049	14977707527239924469524584856128453440584278813225 257149267630529	65	213.186

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:40:41	alpertron	Manual testing	1500000	50000000	12	-	skipped known factor: 360538103	-	-	0.088	-	-	6.144%
2022-12-19T18:06:17	USAFSS	USAFSACS	2000000	6733146420			550097583190851024327654398832916947049	39	128.693	7.797	0.016	15.59	11.849%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2015-03-05T12:41:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	75518688565818607	56.068	17	0.011	0.016	0.023
2022-12-23T01:27:57	LordJulius	Manual testing	2¹	2⁶⁰	360538103	28.426	9	7.17281e-11	0.016	1.49534e-10
2022-12-23T01:27:57	LordJulius	Manual testing	2¹	2⁶⁰	75518688565818607	56.068	17	0.029	0.016	0.061
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶⁰	2⁶¹		-	-	0.287	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.574	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶²	2⁶³		-	-	1.835	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	3.670	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	6.985	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	13.97	-	-
2022-12-23T01:27:57	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	27.94	-	-

ECM factoring results:

Total ECM effort:	17.253 GHz-days
Estimated T-Level:	26.502

Digits	B1	Complete	FacMiss
20	11000	24.808	0.000%
25	50000	3.135	4.351%
30	250000	0.300	74.050%
35	1000000	0.023	97.711%
40	3000000	0.001	99.851%

ECM Summary

B1	B2	curves	GHz-days
50000	5000000	281	4.531
250000	25000000	44	3.547
250000	35000000	100	9.175

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2015-05-01T21:55:00	Richard B. Woods	Puttputt	50000	5000000						1	0.016
2015-06-26T10:34:00	TJAOI	Manual testing	50000	5000000						99	1.596
2016-04-01T10:54:12	TJAOI	Manual testing	50000	5000000						90	1.451
2016-12-30T15:05:45	TJAOI	Manual testing	50000	5000000						91	1.467
2019-03-22T12:39:36	TJAOI	Manual testing	250000	25000000						44	3.547
2021-07-09T11:22:33	TJAOI	Manual testing	250000	35000000						100	9.175

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-27T10:20:49

Oliver Kruse

GTX-1

360538103

75518688565818607

4591CD73B8CFB7__

2017-09-28T09:42:56

Oliver Kruse

Manual testing

360538103

75518688565818607

4591CD73B8CFB7__

2017-11-07T08:06:55

kkmrkkblmbrbk

c4.xlarge

360538103

75518688565818607

4591CD73B8CFB7__

2020-04-19T04:03:44

Oliver Kruse

AddPrpType5

360538103

75518688565818607

A810B1AE2F3559__

2022-12-19T23:35:20

LordJulius

WhiteBox

360538103

75518688565818607

550097583190851024327654398832916947049

A810B1AE2F3559F6

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 = 2000000, B2 = 6733146420 (P-1 stage 2)

B1 = 1500000, B2 = 50000000 (P-1 stage 2)

B1 = 2000000 (P-1 stage 1)

B1 = 1500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

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