M1938887 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	15.3252	68.6567%	1415608	14156080	0.1660	5.5755%	15.4912	70.4043%	1.7475%
PrimeNet	2⁵⁸	0.0198	63.7931%	8000	140000	0.0012	2.4640%	0.0210	64.6853%	0.8921%
GPU72	2⁶²	0.3169	66.1290%	8000	90000	0.0010	1.1517%	0.3178	66.5191%	0.3901%
Difference	+5	+15.0084	+2.5277%	+1407608	+14066080	+0.1650	+4.4238%	+15.1734	+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
1938887	5970727115816410715582161	25	82.304	1539730555678698840 2³ × 3² × 5 × 23 × 185957796579553	2017-06-01	23	185957796579553	715,110	796,969	1,488,515

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2012-01-27T19:07:00	markr	tiny	275000	6000000		-		-	-	0.046	-	-	3.946%
2015-10-08T11:15:52	Bruno Victal	5820K-linux	500000	15000000	12	-		-	-	0.101	-	-	5.104%
2016-12-16T01:10:43	Jocelyn Larouche	low 4M	568903	568903		-		-	-	0.045	-	-	2.124%
2016-12-18T04:24:51	Jocelyn Larouche	low 4M	682683	682683		-		-	-	0.054	-	-	2.288%
2016-12-24T21:06:39	Jocelyn Larouche	low 4M	819219	819219		-		-	-	0.064	-	-	2.458%
2017-01-04T23:07:21	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%
2017-04-07T19:58:15	Jocelyn Larouche	low 4M	1415608	14156080	12	-		-	-	0.166	-	-	5.576%

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	-	-
2010-01-30T08:11:00	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	-	-
2015-05-07T16:29:00	lycorn	Manual testing	2⁶³	2⁶⁴		-	-	1.013	-	-
2015-05-07T16:29:00	lycorn	Manual testing	2⁶⁴	2⁶⁵		-	-	1.927	-	-
2015-09-05T13:49:00	ramgeis	Manual testing	2⁶⁵	2⁶⁶		-	-	3.854	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.886 GHz-days
Estimated T-Level:	24.589

Digits	B1	Curves	Complete	FacMiss
20	11000	257 / 100	2.570	7.555%
25	50000	257 / 280	0.918	39.872%

New Calculation Method

Total ECM effort:	20.886 GHz-days
Estimated T-Level:	24.589

Digits	B1	Complete	FacMiss
20	11000	9.035	0.012%
25	50000	0.804	44.773%
30	250000	0.050	95.140%
35	1000000	0.002	99.771%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.573
50000	5000000	5970727115816410715582161	2	0.139
50000	6750000		7	0.555
50000	7500000		211	17.62

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-11-17T08:34:00	Lars Fricke	M2008	50000	5000000						3	0.209
2009-08-09T20:44:00	SubPrime	abd1	50000	5000000						3	0.209
2011-01-01T23:50:00	Lupo	yorick	50000	5000000						3	0.209
2012-11-21T03:37:00	Donna Noble	Opt6128x4x4	50000	5000000						3	0.209
2013-12-17T19:00:00	Bruce	apandya-DESK11	50000	5000000						3	0.209
2015-04-28T05:57:00	Sara	Sara	50000	5000000						3	0.209
2015-10-12T22:08:28	Chris Smith	starcraft2	50000	5000000						3	0.209
2016-03-14T02:44:39	Jason U	Server7	50000	5000000						3	0.209
2016-06-22T18:55:28	Bruce	Desk6	50000	5000000						3	0.209
2016-09-23T15:56:58	ANONYMOUS	Gorby	50000	5000000						3	0.209
2017-06-01T16:47:01	Bruce	Desk6	50000	5000000	5970727115816410715582161	82.304	2	2		2	0.139
2021-11-09T09:51:10	Dylan Delgado	colab	50000	6750000						7	0.555
2022-04-07T06:59:04	_p95holder_	TFL15_PRPt13pE_s	50000	5000000						7	0.487
2022-04-07T09:50:31	TJAOI	Manual testing	50000	7500000						211	17.62

date	userid	compid	res64	spent (GHz-days)
1999-03-15T00:00:00	ANONYMOUS	v4_computers	4C1B9C3299F3E337	0.105
2015-07-12T18:10:00	MadPoo	Manual testing	4C1B9C3299F3E337	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)

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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