M1938427 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	15.3289	68.6567%	1415608	14156080	0.1660	5.5754%	15.4948	70.4042%	1.7475%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4639%	0.0210	64.6852%	0.8921%
GPU72	2⁶²	0.3169	66.1290%	8000	90000	0.0010	1.1516%	0.3179	66.5191%	0.3901%
Difference	+5	+15.0119	+2.5277%	+1407608	+14066080	+0.1650	+4.4237%	+15.1769	+3.8851%	+3.8851%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1938427	1167457327669960779584633	25	79.950	301135231729118708 2² × 23 × 337 × 9712786470427	2017-09-30	337	9712786470427	115,768	41,627	77,747

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-27T13:15:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.946%
2015-10-08T11:03:55	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	5.104%
2016-12-14T20:31:00	Jocelyn Larouche	low 4M	568903	568903		-		-	-	0.045	-	-	2.124%
2016-12-18T04:24:52	Jocelyn Larouche	low 4M	682683	682683		-		-	-	0.054	-	-	2.288%
2016-12-24T02:11:55	Jocelyn Larouche	low 4M	819219	819219		-		-	-	0.064	-	-	2.458%
2017-01-04T23:07:26	Jocelyn Larouche	low 4M	983062	983062		-		-	-	0.077	-	-	2.636%
2017-01-22T06:40:05	Jocelyn Larouche	low 4M	1179674	1179674		-		-	-	0.093	-	-	2.820%
2017-04-07T19:58:14	Jocelyn Larouche	low 4M	1415608	14156080	12	-		-	-	0.166	-	-	5.575%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-12-21T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.020	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.059	-	-
2010-01-30T19:40:00	S485122	USB-W	2⁶⁰	2⁶¹		-	-	0.079	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.158	-	-
2011-08-27T22:21:00	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.823	-	-
2016-02-23T16:28:59	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.506	-	-
2015-05-07T23:03:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.013	-	-
2015-05-07T23:04:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.928	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.855	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	21.102 GHz-days
Estimated T-Level:	24.643

Digits	B1	Curves	Complete	FacMiss
20	11000	260 / 100	2.600	7.331%
25	50000	260 / 280	0.929	39.446%

New Calculation Method

Total ECM effort:	21.102 GHz-days
Estimated T-Level:	24.643

Digits	B1	Complete	FacMiss
20	11000	9.135	0.011%
25	50000	0.812	44.394%
30	250000	0.050	95.090%
35	1000000	0.002	99.769%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		40	2.781
50000	5000000	1167457327669960779584633	3	0.209
50000	6771643		2	0.159
50000	7500000		215	17.95

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-13T18:26:00	S36049	Wolle3	50000	5000000						3	0.209
2009-08-08T19:49:00	SubPrime	abd1	50000	5000000						3	0.209
2011-01-01T14:09:00	James Hintz	ryan	50000	5000000						3	0.209
2012-11-20T18:02:00	Donna Noble	PH2x6	50000	5000000						3	0.209
2013-12-18T07:33:00	OS1	L3	50000	5000000						3	0.209
2015-04-09T13:04:00	OS1	L3	50000	5000000						3	0.209
2015-10-12T08:51:46	Chris Smith	starcraft2	50000	5000000						3	0.209
2016-03-13T20:37:09	Bruce	Desk6	50000	5000000						3	0.209
2016-06-22T15:48:14	Jason U	Server7	50000	5000000						3	0.209
2016-09-24T02:34:48	Bruce	Desk6	50000	5000000						3	0.209
2017-06-01T13:29:48	Bruce	Desk6	50000	5000000						3	0.209
2017-09-30T22:22:30	Bruce	Desk6	50000	5000000	1167457327669960779584633	79.950	3	2		3	0.209
2022-02-04T06:47:54	carlos56	febrero2022	50000	6771643						2	0.159
2022-03-17T10:42:01	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.487
2022-04-07T09:50:30	TJAOI	Manual testing	50000	7500000						215	17.95

date	userid	compid	res64	spent (GHz-days)
1998-12-21T00:00:00	ANONYMOUS	v4_computers	5FF935055475E75A	0.105
2015-07-12T18:10:00	MadPoo	Manual testing	5FF935055475E75A	0.105

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 = 1415608, B2 = 14156080 (P-1 stage 2)

B1 = 1415608 (P-1 stage 1)

B1 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 1179674 (P-1 stage 1)

B1 = 983062 (P-1 stage 1)

B1 = 819219 (P-1 stage 1)

B1 = 682683 (P-1 stage 1)

B1 = 275000, B2 = 6000000 (P-1 stage 2)

B1 = 568903 (P-1 stage 1)

B1 = 500000 (P-1 stage 1)

B1 = 275000 (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