M1862957 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	15.9499	68.6567%	500000	15000000	0.1015	5.0795%	16.0513	70.2488%	1.5921%
PrimeNet	2⁵⁷	0.0103	63.1579%	9000	160000	0.0014	3.0270%	0.0117	64.2731%	1.1152%
GPU72	2⁶¹	0.1649	65.5738%	10000	150000	0.0014	1.6884%	0.1663	66.1550%	0.5812%
Difference	+6	+15.7850	+3.0829%	+490000	+14850000	+0.1001	+3.3911%	+15.8851	+4.0938%	+4.0938%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1862957	965011727	9	29.846	259 7 × 37	-	7	37	4.054e-11	6.792e-7	1.121e-6
1862957	893641355081341040833	21	69.598	239844868958688 2⁵ × 3 × 7 × 356912007379	2020-12-02	32	356912007379	101.43	1,529.6	2,856.9
1862957	9037620597292984135799	22	72.936	2425611701529607 30829 × 78679545283	2021-08-27	30829	78679545283	647.48	337.20	629.80
1862957	2165624752073048918885466559	28	90.807	581233155696306709947 3² × 13 × 17167 × 289381065389473	2021-08-27	17167	289381065389473	252,495,557	1,240,215	2,316,376

exponent	prime factors	composite factor	digits	bits*
1862957	965011727 893641355081341040833	862374387385665143290230848591	30	99.444
1862957	965011727 9037620597292984135799	8721409860564474145870995514873	31	102.782
1862957	965011727 2165624752073048918885466559	2089853282031959767369146999301337393	37	120.653
1862957	893641355081341040833 9037620597292984135799	8076391517275941141146492839499447676080567	43	142.535
1862957	893641355081341040833 2165624752073048918885466559	1935291838040252666241422799101816685225875003647	49	160.405
1862957	9037620597292984135799 2165624752073048918885466559	19572094865342899054358920728791825393049529245641	50	163.743
1862957	965011727 893641355081341040833 9037620597292984135799	77938125260146062961681278150384958174406445518092 09	52	172.381
1862957	965011727 893641355081341040833 2165624752073048918885466559	18675793188762285209659900142984181682472370223555 22768369	58	190.251
1862957	965011727 9037620597292984135799 2165624752073048918885466559	18887301067012383463633568970347498046029180013873 028632007	59	193.589
1862957	893641355081341040833 9037620597292984135799 2165624752073048918885466559	17490433377245585418194730964942320414806654885239 399116316112268258953	71	233.342
1862957	965011727 893641355081341040833 9037620597292984135799 2165624752073048918885466559	16878473319354204887538114550779365078879926401897 859349678485377918459517741831	80	263.188

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:37:14	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 965011727	-	-	0.101	-	-	5.079%

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.792 GHz-days
Estimated T-Level:	24.607

Digits	B1	Curves	Complete	FacMiss
20	11000	258 / 100	2.580	7.480%
25	50000	258 / 280	0.921	39.729%

New Calculation Method

Total ECM effort:	19.792 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	10.625	0.002%
25	50000	0.978	37.611%
30	250000	0.062	93.983%
35	1000000	0.003	99.709%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		33	2.284
50000	5000000	893641355081341040833	6	0.415
50000	6600000		7	0.546
50000	6600000	9037620597292984135799	12	0.937
50000	6600000	2165624752073048918885466559	200	15.61

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-18T02:13:49	alpertron	laptop2	50000	5000000						3	0.208
2019-01-17T21:57:47	tottenhoff	i7-8700k-01	50000	5000000						3	0.208
2020-06-30T13:27:17	argusdusty	Argus-PC	50000	5000000						3	0.208
2020-07-13T17:35:17	argusdusty	Manual testing	50000	5000000						3	0.208
2020-10-07T09:13:11	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.484
2020-12-02T20:22:02	Poao	servarica-CA	50000	5000000	893641355081341040833	69.598	6	2	5421983898687947	6	0.415
2021-02-20T17:17:33	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.484
2021-06-11T09:32:40	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						7	0.484
2021-08-27T10:07:51	TJAOI	Manual testing	50000	6600000	9037620597292984135799	72.936	12	2		12	0.937
2021-08-27T10:07:51	TJAOI	Manual testing	50000	6600000	2165624752073048918885466559	90.807	200	2		200	15.61
2021-08-27T10:07:51	TJAOI	Manual testing	50000	6600000						7	0.546

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-04T09:21:48

Oliver Kruse

GTX-3

965011727

96B94CF8CD213C__

2017-11-07T12:21:58

kkmrkkblmbrbk

old

965011727

96B94CF8CD213C__

2020-12-03T15:56:10

Poao

pc-Home

965011727

893641355081341040833

83F7DD895D0C7380

2021-08-28T06:52:50

SRJ2877

LTOS

965011727

893641355081341040833

9037620597292984135799

2165624752073048918885466559

83F7DD895D0C7380

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

10¹⁵

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