M1804093 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	16.4703	68.6567%	2780000	91760000	0.6000	8.1178%	17.0703	71.2011%	2.5444%
PrimeNet	2⁵⁷	0.0106	63.1579%	8000	150000	0.0012	2.8714%	0.0119	64.2158%	1.0579%
GPU72	2⁶¹	0.1703	65.5738%	9000	130000	0.0012	1.5551%	0.1715	66.1091%	0.5354%
Difference	+6	+16.3000	+3.0829%	+2771000	+91630000	+0.5988	+6.5627%	+16.8988	+5.0920%	+5.0920%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1804093	14516043819142743992921	23	73.620	4023086342872220 2² × 5 × 13² × 1190262231619	2017-04-21	169	1190262231619	1,698.3	5,101.2	9,527.6
1804093	140492699696158743152017	24	76.895	38937211024087656 2³ × 3² × 7 × 169313 × 456293203	2021-01-08	169313	456293203	12,956	1.9682	3.6524

exponent	prime factors	composite factor	digits	bits*
1804093	14516043819142743992921 140492699696158743152017	2039398185059102790505525612716306771874871657	46	150.515

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-09-21T00:00:00	ANONYMOUS	v4_computers	25000	387500		-		-	-	0.004	-	-	1.199%
2011-02-11T15:53:00	Carsten Kossendey	leela	100000	1650000		-		-	-	0.015	-	-	2.477%
2014-05-12T10:21:00	Jocelyn Larouche	Manual testing	135577	135577		-		-	-	0.011	-	-	1.060%
2014-09-20T22:31:00	Jocelyn Larouche	Manual testing	171154	171154		-		-	-	0.013	-	-	1.201%
2015-05-02T11:15:00	mikr	MSI	2780000	91760000		-		-	-	0.600	-	-	8.118%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-01-25T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.021	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.064	-	-
2010-04-12T13:46:00	Architects Cubed	m1_tt	2⁶⁰	2⁶¹		-	-	0.085	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.170	-	-
2010-12-13T03:33:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.885	-	-
2016-02-23T16:28:52	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.544	-	-
2015-04-20T21:13:00	snme2pm1	Manual testing	2⁶³	2⁶⁴		-	-	1.088	-	-
2015-04-20T21:13:00	snme2pm1	Manual testing	2⁶⁴	2⁶⁵		-	-	2.071	-	-
2015-08-31T08:30:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	4.142	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.309 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	17.309 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	8.097	0.030%
25	50000	0.732	48.105%
30	250000	0.045	95.594%
35	1000000	0.002	99.794%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		107	7.379
50000	5000000	14516043819142743992921	2	0.138
50000	5000000	140492699696158743152017	142	9.79

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-09-14T21:03:00	Scott Kurowski	HomeOffice	50000	5000000						3	0.207
2009-07-15T19:32:00	SubPrime	abd1	50000	5000000						3	0.207
2010-10-14T00:48:00	unconnected	X3220--xp	50000	5000000						3	0.207
2012-03-27T16:53:00	S36049	Wolle5	50000	5000000						3	0.207
2013-07-17T12:55:00	OS1	L3	50000	5000000						3	0.207
2014-03-26T03:36:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2014-07-12T21:49:00	mikr	MSI	50000	5000000						12	0.828
2016-05-19T11:09:10	Bruce	DESK3	50000	5000000						3	0.207
2016-08-17T22:39:49	Bruce	DESK3	50000	5000000						3	0.207
2016-10-26T00:03:10	Bruce	DESK3	50000	5000000						3	0.207
2016-12-29T12:40:00	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2017-04-21T09:04:43	Chang Chia-Tche	exbpc13	50000	5000000	14516043819142743992921	73.620	2	2		2	0.138
2021-01-08T11:40:05	TJAOI	Manual testing	50000	5000000	140492699696158743152017	76.895	142	2		142	9.79
2021-01-08T11:40:05	TJAOI	Manual testing	50000	5000000						65	4.482

date	userid	compid	res64	spent (GHz-days)
1998-12-27T00:00:00	ANONYMOUS	v4_computers	93B4094088B5F00D	0.098
2015-07-01T17:35:00	MadPoo	Manual testing	93B4094088B5F00D	0.098

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-03T19:32:12

Oliver Kruse

GTX-3

14516043819142743992921

698EAA401FC6CD__

2017-11-05T13:22:12

kkmrkkblmbrbk

c4.xlarge

14516043819142743992921

698EAA401FC6CD__

2021-01-08T17:53:18

SRJ2877

LTOS

14516043819142743992921

140492699696158743152017

5306867F817D9033

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 = 2780000, B2 = 91760000 (P-1 stage 2)

B1 = 2780000 (P-1 stage 1)

B1 = 100000, B2 = 1650000 (P-1 stage 2)

B1 = 171154 (P-1 stage 1)

B1 = 135577 (P-1 stage 1)

B1 = 100000 (P-1 stage 1)

B1 = 25000, B2 = 387500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

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