M2 297 543 Mersenne number exponent details

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	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁶⁷	12.9329	67.1642%	500000	15000000	0.1264	5.2091%	13.0593	68.8746%
Target	2⁶²	0.2674	64.5161%	12000	1000000	0.0064	1.7372%	0.2738	65.1325%
Difference	+5	+12.6655	+2.6481%	+488000	+14000000	+0.1199	+3.4719%	+12.7854	+3.7421%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
2297543	211008596033428016100743	24	77.482	45920488981800997 23 × 47 × 42479638281037	2015-04-12	47	42479638281037	21,388	226,709	423,429

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2003-08-08	ANONYMOUS	v4_computers	2048	204800		-		-	-	0.001	-	-	0.284%
2010-11-07	Jocelyn Larouche	Manual testing	15000	15000		-		-	-	0.001	-	-	0.241%
2010-11-15	Jocelyn Larouche	Manual testing	20000	20000		-		-	-	0.002	-	-	0.308%
2010-12-04	Oscar Östlin		75011	75011		-		-	-	0.007	-	-	0.787%
2011-01-17	Oscar Östlin		90000	1755000		-		-	-	0.018	-	-	2.557%
2013-11-13	c10ck3r	Manual testing	500000	10000000		-		-	-	0.100	-	-	4.819%
2016-04-28	alpertron	Manual testing	500000	15000000	12	-		-	-	0.126	-	-	5.209%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-11-07	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.017	-	-
2022-03-09	LordJulius	Manual testing	2¹	2⁶⁰		-	-	0.067	-	-
2009-01-15	Sturle Sunde	gonsha.ifi	2⁶⁰	2⁶¹		-	-	0.067	-	-
2012-05-12	Sebastian Hornbostel	Manual testing	2⁶¹	2⁶²		-	-	0.134	-	-
2013-12-06	Jerry Hallett	Manual testing	2⁶²	2⁶³		-	-	0.427	-	-
2015-03-12	VictordeHollander	Manual testing	2⁶³	2⁶⁴		-	-	0.855	-	-
2015-03-12	VictordeHollander	Manual testing	2⁶⁴	2⁶⁵		-	-	1.626	-	-

ECM factoring results:

Total ECM effort:	8.255 GHz-days
Estimated T-Level:	21.409

Digits	B1	Complete	FacMiss
20	11000	3.010	4.928%
25	50000	0.282	75.446%
30	250000	0.018	98.220%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		12	1.062
50000	5000000	211008596033428016100743	3	0.265
50000	7050000		50	5.176
50000	27023535		7	1.751

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2009-01-17	S36049	Wolle3	50000	5000000						3	0.265
2010-01-10	lindee	tanagra	50000	5000000						3	0.265
2011-11-19	S36049	Wolle5	50000	5000000						3	0.265
2013-09-19	arnaud	srv-630	50000	5000000						3	0.265
2015-04-12	Jason U	Server7	50000	5000000	211008596033428016100743	77.482	3	2		3	0.265
2022-12-07	Nesowa	309b3ECMtrial	50000	27023535						7	1.751
2023-09-23	SmithMichae2	smithBee	50000	7050000						50	5.176

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-11-07	ANONYMOUS	v4_computers	A15EA30E806CE795	0.155
1999-03-15	ANONYMOUS	v4_computers	A15EA30E806CE795	0.155

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-12

kkmrkkblmbrbk

c4.xlarge

D50270E36BA4C3__

2017-10-30

Oliver Kruse

GTX-2

211008596033428016100743

D50270E36BA4C3__

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, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 90000, B2 = 1755000 (P-1 stage 2)

B1 = 90000 (P-1 stage 1)

B1 = 75011 (P-1 stage 1)

B1 = 20000 (P-1 stage 1)

B1 = 15000 (P-1 stage 1)

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

B1 = 2048 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

10¹⁴

TF factor-bounds graph:

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

this exponent TF target: 62

TF double-checked to: 67.9

ECM T-Level=21.41 ~= 55-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

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