M5 273 Mersenne number exponent details

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	5,635.1067	80.5970%	59000000000	241667483419362000	1,209,678.4265	39.9482%	1,215,313.5331	88.3482%
Target	2⁴⁴	0.0004	70.4545%	500	80000	0.0000	1.0359%	0.0004	70.7606%
Difference	+23	+5,635.1062	+10.1425%	+58999999500	+241667483419282000	+1,209,678.4265	+38.9123%	+1,215,313.5327	+17.5875%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
5273	38134337	8	25.185	3616 2⁵ × 113	-	32	113	1.511e-9	3.345e-9	5.983e-9
5273	10372530354079	14	43.238	983551143 3 × 71 × 1583 × 2917	2003-02-02	1583	2917	0.0004	1.521e-7	2.960e-7
5273	105636369464519254639	21	66.518	10016723825575503 3 × 23 × 145169910515587	2003-01-25	23	145169910515587	5,232.0	726.65	1,357.2
5273	14295639336224604778372751	26	83.564	1355550856839048433375 5³ × 7 × 133481 × 975049 × 11903149	2003-02-02	975049	11903149	554,439,647	0.0001	0.0002

exponent	prime factors	composite factor	digits	bits*
5273	38134337 10372530354079	395549568065177910623	21	68.422
5273	38134337 105636369464519254639	4028372912616486799392439343	28	91.702
5273	38134337 14295639336224604778372751	545154728078045386310276798251087	33	108.748
5273	10372530354079 105636369464519254639	1095716448765429967948179833322481	34	109.756
5273	10372530354079 14295639336224604778372751	148281952945955480332886546251475301329	39	126.802
5273	38134337 10372530354079 105636369464519254639	41784420313664140347635088300523320130097	41	134.940
5273	105636369464519254639 14295639336224604778372751	1510139438652937146298369268123187081827941889	46	150.081
5273	38134337 10372530354079 14295639336224604778372751	5654633964659209074011167737519845888056633873	46	151.986
5273	38134337 105636369464519254639 14295639336224604778372751	57588166270581931176760316221052973692473312011542 593	53	175.266
5273	10372530354079 105636369464519254639 14295639336224604778372751	15663967166319412436887556008866093789662740828465 006115231	59	193.319
5273	38134337 10372530354079 105636369464519254639 14295639336224604778372751	59733500267735952351026129194847460844860607509634 3735905279786847	66	218.504

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2021-11-19	nordi	sweet16	1000000	1000000		-	skipped known factor: 38134337 skipped known factor: 10372530354079	-	-	9.18736e-5	-	-	1.125%
2021-11-19	nordi	sweet16	100000000	100000000		-	skipped known factor: 38134337 skipped known factor: 10372530354079 skipped known factor: 14295639336224604778372751	-	-	0.009	-	-	5.329%
2022-01-24	Ethan O'Connor	Highland2017HiveOS	130000000	184786243171530		-	skipped known factor: 38134337 skipped known factor: 10372530354079 skipped known factor: 105636369464519254639 skipped known factor: 14295639336224604778372751	-	-	925.0	-	-	24.075%
2022-01-24	Ethan O'Connor	Highland2017HiveOS	1300000000	1300000000		-	skipped known factor: 38134337 skipped known factor: 10372530354079 skipped known factor: 14295639336224604778372751	-	-	0.119	-	-	8.997%
2023-06-29	-Anonymous-	GreatLakes	59000000000	241667483419362000		-	skipped known factor: 38134337 skipped known factor: 10372530354079 skipped known factor: 105636369464519254639 skipped known factor: 14295639336224604778372751	-	-	1,209,678	-	-	39.948%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-16	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-01-25	ANONYMOUS	v4_computers	?	?	105636369464519254639	66.518	21	2,431	7.61696e-7	5,543
2003-01-25	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-01-25	ANONYMOUS	v4_computers	?	?	38134337 105636369464519254639	91.702	28	8.66029e+10	7.61696e-7	1.97439e+11
2003-01-25	ANONYMOUS	v4_computers	?	?	38134337 14295639336224604778372751	108.748	33	9.62015e+12	7.61696e-7	2.19322e+13
2003-02-02	ANONYMOUS	v4_computers	?	?	10372530354079	43.238	14	0.000	7.61696e-7	0.000
2003-02-02	ANONYMOUS	v4_computers	?	?	14295639336224604778372751	83.564	26	182,936,950	7.61696e-7	417,063,636
2003-02-02	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-02-09	ANONYMOUS	v4_computers	?	?	105636369464519254639	66.518	21	2,431	7.61696e-7	5,543
2003-02-09	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-02-16	ANONYMOUS	v4_computers	?	?	105636369464519254639	66.518	21	2,431	7.61696e-7	5,543
2003-02-16	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-02-27	ANONYMOUS	v4_computers	?	?	105636369464519254639	66.518	21	2,431	7.61696e-7	5,543
2003-02-27	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537
2003-02-27	ANONYMOUS	v4_computers	?	?	38134337 10372530354079 105636369464519254639	134.940	41	6.36600e+12	7.61696e-7	1.45134e+13
2003-03-07	ANONYMOUS	v4_computers	?	?	105636369464519254639	66.518	21	2,431	7.61696e-7	5,543
2003-03-07	ANONYMOUS	v4_computers	?	?	38134337 10372530354079	68.422	21	10,324	7.61696e-7	23,537

ECM factoring results:

Total ECM effort:	15.426 GHz-days
Estimated T-Level:	38.089

Digits	B1	Complete	FacMiss
20	11000	249.167	0.000%
25	50000	73.478	0.000%
30	250000	17.768	0.000%
35	1000000	3.515	2.976%
40	3000000	0.618	53.912%
45	11000000	0.100	90.502%
50	44000000	0.015	98.535%
55	110000000	0.002	99.795%

ECM Summary

B1	B2	curves	GHz-days
3000000	300000000	890	3.530
11000000	1100000000	18	0.262
44000000	4400000000	200	11.63

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-05-07	unconnected	E5430-next	44000000	4400000000						200	11.63
2009-10-13	Carsten Kossendey	durandal	3000000	300000000						1	0.004
2016-10-04	kkmrkkblmbrbk	old	3000000	300000000						889	3.526
2016-10-04	kkmrkkblmbrbk	old	11000000	1100000000						18	0.262

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-21

Oliver Kruse

Oliver-PC

BDD2290AB18AB3__

2017-09-21

Oliver Kruse

Manual testing

BDD2290AB18AB3__

2017-10-02

kkmrkkblmbrbk

Manual testing

38134337

10372530354079

105636369464519254639

14295639336224604778372751

BDD2290AB18AB3__

2017-12-07

ATH

Manual testing

38134337

10372530354079

105636369464519254639

14295639336224604778372751

BDD2290AB18AB3__

2020-04-17

Oliver Kruse

IOS-1

38134337

10372530354079

105636369464519254639

14295639336224604778372751

34F16B85C416E4__

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 = 59000000000, B2 = 241667483419362000 (P-1 stage 2)

B1 = 130000000, B2 = 184786243171530 (P-1 stage 2)

B1 = 59000000000 (P-1 stage 1)

B1 = 1300000000 (P-1 stage 1)

B1 = 130000000 (P-1 stage 1)

B1 = 100000000 (P-1 stage 1)

B1 = 1000000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

10¹⁶

10¹⁷

10¹⁸

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