M1806251 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	16.4506	68.6567%	500000	15000000	0.1015	5.0606%	16.5521	70.2429%	1.5862%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8720%	0.0119	64.2160%	1.0581%
GPU72	2⁶¹	0.1701	65.5738%	9000	130000	0.0012	1.5555%	0.1713	66.1093%	0.5355%
Difference	+6	+16.2805	+3.0829%	+491000	+14870000	+0.1002	+3.5051%	+16.3808	+4.1336%	+4.1336%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1806251	3612503	7	21.785	1 1	-	1	1	1.547e-13	7.866e-8	1.601e-7
1806251	266435654031344076887	21	67.852	73753773432193 73753773432193	2020-10-05	1	73753773432193	23.375	316,090	590,369
1806251	1254092859361788461647	22	70.087	347153540499573 3 × 115717846833191	2020-10-15	3	115717846833191	210.61	495,938	926,274
1806251	1200724890291139991363519	25	79.990	332380408451300509 23 × 67 × 12384121 × 17416769	2019-09-16	12384121	17416769	91,390	0.9957	1.9826

exponent	prime factors	composite factor	digits	bits*
1806251	3612503 266435654031344076887	962499599495192571786518161	27	89.637
1806251	3612503 1254092859361788461647	4530414216723038903065172441	28	91.872
1806251	3612503 1200724890291139991363519	4337622268351414092220686478057	31	101.775
1806251	266435654031344076887 1254092859361788461647	334135051200096514395845937429693018652889	42	137.939
1806251	266435654031344076887 1200724890291139991363519	319915921456433747285913668210604655502885353	45	147.843
1806251	1254092859361788461647 1200724890291139991363519	1505820510972085505058005234440149404966455793	46	150.077
1806251	3612503 266435654031344076887 1254092859361788461647	1207063874865502258544536636502578318962617471167	49	159.724
1806251	3612503 266435654031344076887 1200724890291139991363519	11556972260091312813716049841518139498181398463685 59	52	169.627
1806251	3612503 1254092859361788461647 1200724890291139991363519	54397811133481918032785590834307430458895364515798 79	52	171.862
1806251	266435654031344076887 1254092859361788461647 1200724890291139991363519	40120427269466033115798060775476087403308900061907 9512031678556391	66	217.930
1806251	3612503 266435654031344076887 1254092859361788461647 1200724890291139991363519	14493516387222785302891984194558969217271561140034 26594452974879998156673	73	239.714

	GHz-Days	worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved
2016-03-16T12:36:25	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 3612503	-	-	0.101	-	-	5.061%

ECM factoring results:

Old Calculation Method

Total ECM effort:	18.081 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:	18.081 GHz-days
Estimated T-Level:	24.607

Digits	B1	Complete	FacMiss
20	11000	8.400	0.022%
25	50000	0.760	46.789%
30	250000	0.047	95.427%
35	1000000	0.002	99.786%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		218	15.04
50000	5000000	266435654031344076887	1	0.069
50000	5000000	1254092859361788461647	2	0.138
50000	5000000	1200724890291139991363519	2	0.138
50000	6500000		35	2.701

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-13T04:58:09	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-03-31T12:49:24	Hexaflexagon	crou	50000	5000000						3	0.207
2019-09-17T00:24:10	Chang Chia-Tche	exbpc13	50000	5000000	1200724890291139991363519	79.990	2	2		2	0.138
2020-04-20T00:11:22	Team_Inspector	SpudBoy4	50000	5000000						3	0.207
2020-05-02T22:31:48	Oliver Kruse	IOS-2	50000	5000000						3	0.207
2020-05-31T10:07:49	_p95holder_	TFL17_PRPt12pE_k	50000	5000000						3	0.207
2020-06-28T23:55:29	MarkS	desktop-i7	50000	5000000						3	0.207
2020-07-25T23:25:42	Ahmed Azhad	c5.4xlarge.azf	50000	5000000						3	0.207
2020-10-05T07:46:38	nordi	sweet16	50000	5000000	266435654031344076887	67.852	1	2	7849581937938828	1	0.069
2020-10-15T01:41:20	nordi	sweet16	50000	5000000	1254092859361788461647	70.087	2	2	734614809215734	2	0.138
2020-10-31T04:43:41	Ahmed Azhad	c5.large.az	50000	5000000						7	0.483
2021-01-20T01:48:24	Chang Chia-Tche	exbpc13	50000	5000000						7	0.483
2021-02-26T17:52:37	TJAOI	Manual testing	50000	5000000						185	12.76
2021-02-26T17:52:37	TJAOI	Manual testing	50000	6500000						35	2.701

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T20:04:27

Oliver Kruse

GTX-2

3612503

A51720BD1C85A5__

2017-11-05T14:57:57

ATH

ec2-1xf

3612503

A51720BD1C85A5__

2019-09-17T19:30:48

mnd9

27016b

3612503

1200724890291139991363519

0CE86BB044F6C95B

2019-09-17T20:08:06

ATH

ec2-PRPCFDC

3612503

1200724890291139991363519

0CE86BB044F6C95B

2020-10-05T09:46:26

M Miller

cruncher

3612503

266435654031344076887

1200724890291139991363519

0CE86BB044F6C95B

2020-10-05T21:12:00

kotenok2000

shodan1

3612503

266435654031344076887

1200724890291139991363519

0CE86BB044F6C95B

2020-10-15T12:36:04

tottenhoff

3-of-4-Ryzen-5-3600

3612503

266435654031344076887

1254092859361788461647

1200724890291139991363519

0CE86BB044F6C95B

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

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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