M1248241 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	23.8046	68.6567%	4218475	156083565	0.5741	8.7493%	24.3787	71.3990%	2.7423%
PrimeNet	2⁵⁶	0.0077	62.5000%	5500	90000	0.0005	2.4357%	0.0082	63.4134%	0.9134%
GPU72	2⁶⁰	0.1230	65.0000%	5000	32000	0.0003	0.8551%	0.1233	65.2993%	0.2993%
Difference	+7	+23.6816	+3.6567%	+4213475	+156051565	+0.5738	+7.8942%	+24.2554	+6.0998%	+6.0998%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1248241	30732095641367625571793	23	74.702	12310161115268456 2³ × 11 × 139888194491687	2018-10-05	11	139888194491687	5,809.0	350,261	654,189
1248241	120089455779008969959790436223	30	96.600	48103473519540285073071 3 × 13 × 23 × 727 × 1181 × 604861 × 103262849	2015-07-20	604861	103262849	2.335e+10	0.2848	0.4829

exponent	prime factors	composite factor	digits	bits*
1248241	30732095641367625571793 120089455779008969959790436223	36906006405202917798482439711506907232779332742578 39	52	171.302

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-02-24T00:00:00	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.238%
2003-11-28T00:00:00	eteo	v4_computers	200000	2000000		-		-	-	0.014	-	-	2.760%
2014-09-25T21:17:00	Jocelyn Larouche	Manual testing	251419	251419		-		-	-	0.012	-	-	1.372%
2015-01-17T16:24:00	mikr	MSI	4218475	156083565	12		120089455779008969959790436223	30	96.600	0.574	0.079	1.148	8.749%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-11-17T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.015	-	-
2003-06-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.031	-	-
2022-03-07T17:31:42	LordJulius	Manual testing	2⁵⁸	2⁶⁰		-	-	0.092	-	-
2009-02-17T05:53:00	Sturle Sunde	goscha.ifi	2⁶⁰	2⁶¹		-	-	0.123	-	-
2012-09-14T15:01:00	Axelsson	Manual testing	2⁶¹	2⁶²		-	-	0.246	-	-
2012-10-07T08:33:00	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.786	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	19.207 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	325 / 100	3.250	3.815%
25	50000	325 / 280	1.161	31.261%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	19.207 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.731	0.000%
25	50000	1.349	25.941%
30	250000	0.108	89.793%
35	1000000	0.007	99.295%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		153	5.866
50000	5000000	30732095641367625571793	128	4.907
250000	25000000		44	8.434

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-11-08T13:16:00	James Heinrich	WHS	50000	5000000						1	0.038
2008-08-26T16:56:00	Sturle Sunde	v21	50000	5000000						3	0.115
2009-01-31T18:43:00	Sturle Sunde	v23	50000	5000000						3	0.115
2009-07-03T02:40:00	Lupo	yorick	50000	5000000						3	0.115
2009-10-12T06:24:00	James Hintz	jeff4	50000	5000000						3	0.115
2010-03-18T12:35:00	Lackó	Iroda_Eva	50000	5000000						3	0.115
2010-12-09T20:23:00	Donna Noble	PH9550v2	50000	5000000						3	0.115
2011-09-21T01:04:00	OS1	Tina	50000	5000000						3	0.115
2012-06-23T20:13:00	soldake	athlonx3_435_unlock	50000	5000000						3	0.115
2012-11-18T21:11:00	Salvetay	server5	50000	5000000						3	0.115
2013-09-03T19:52:00	OS1	Tina	50000	5000000						3	0.115
2014-02-05T22:36:00	jim f in mn	asus	50000	5000000						3	0.115
2014-03-09T11:20:00	Bruce	snowflake	50000	5000000						3	0.115
2014-09-14T12:47:00	zampel	dufay	50000	5000000						3	0.115
2017-11-24T16:14:30	TJAOI	Manual testing	50000	5000000						100	3.834
2018-10-05T13:08:20	TJAOI	Manual testing	50000	5000000	30732095641367625571793	74.702	128	2		128	4.907
2018-10-05T13:08:20	TJAOI	Manual testing	50000	5000000						13	0.498
2021-01-15T10:44:37	TJAOI	Manual testing	250000	25000000						44	8.434

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T18:28:58

Oliver Kruse

GTX-0

120089455779008969959790436223

1438AE9C2EC1A6__

2017-10-20T15:11:50

kkmrkkblmbrbk

c4.xlarge

120089455779008969959790436223

1438AE9C2EC1A6__

2018-10-07T16:55:32

Oliver Kruse

GTX-3

30732095641367625571793

120089455779008969959790436223

098E076BE9D575__

2018-10-07T17:04:25

ATH

ec2-PRPCFDC

30732095641367625571793

120089455779008969959790436223

098E076BE9D575__

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 = 4218475, B2 = 156083565 (P-1 stage 2)

B1 = 4218475 (P-1 stage 1)

B1 = 200000, B2 = 2000000 (P-1 stage 2)

B1 = 251419 (P-1 stage 1)

B1 = 200000 (P-1 stage 1)

B1 = 2048, B2 = 204800 (P-1 stage 2)

B1 = 2048 (P-1 stage 1)

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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