M13 714 843 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	2⁷²	69.7298	66.6667%	1600000	1656779670	59.0447	9.2152%	128.7745	69.7384%
Target	2⁶⁹	8.7049	65.2174%	90000	17600000	0.6716	2.7890%	9.3766	66.1875%
Difference	+3	+61.0249	+1.4493%	+1510000	+1639179670	+58.3730	+6.4262%	+119.3979	+3.5509%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
13714843	2477183574878962121484054480461935528241	40	130.864	90310314703528218350150070272840 2³ × 5 × 7 × 11 × 31 × 2467 × 22669 × 75029 × 152833 × 1474949453	2023-06-28	152833	1474949453	1.248e+10	51.791	96.558

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-02-24	ANONYMOUS	v4_computers	165000	3712500		-		-	-	0.230	-	-	2.493%
2023-03-09	nordi	sweet16_30.8b14	1600000	1600000		-		-	-	1.029	-	-	2.416%
2023-06-28	nordi	sweet16_30.8b14	1600000	1656779670			2477183574878962121484054480461935528241	40	130.864	59.04	12.17	118.1	9.215%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2000-06-28	lalera	v4_computers	2¹	2⁵⁶		-	-	0.001	-	-
2000-07-03	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.532	-	-
2000-10-28	ANONYMOUS	v4_computers	2¹	2⁶⁵		-	-	0.532	-	-
2014-07-02	Nesowa	Manual testing	2⁶⁵	2⁶⁶		-	-	0.545	-	-
2015-08-16	Nesowa	Manual testing	2⁶⁶	2⁶⁷		-	-	1.090	-	-
2017-12-23	-Anonymous-	Manual testing	2⁶⁷	2⁶⁸		-	-	2.179	-	-
2018-01-14	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	4.359	-	-
2021-08-08	SRBase	Manual testing	2⁶⁹	2⁷⁰		-	-	8.718	-	-
2021-09-04	SRBase	Manual testing	2⁷⁰	2⁷¹		-	-	17.44	-	-
2021-09-24	Jon Pace	Manual testing	2⁷¹	2⁷²		-	-	34.87	-	-

ECM factoring results:

Total ECM effort:	0.675 GHz-days
Estimated T-Level:	0.192

Digits	B1	Complete	FacMiss
20	11000	0.038	96.227%
25	50000	0.004	99.645%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		1	0.675

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2016-08-01	BloodIce	URM2	50000	5000000						1	0.675

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2002-03-03	ANONYMOUS	v4_computers	21F365E9813154B7	6.085
2005-03-20	ANONYMOUS	v4_computers	21F365E9813154B7	6.085

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 = 1600000, B2 = 1656779670 (P-1 stage 2)

B1 = 1600000 (P-1 stage 1)

B1 = 165000, B2 = 3712500 (P-1 stage 2)

B1 = 165000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁷

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁷²

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁵⁶

this exponent TF target: 69

TF double-checked to: 67.9

ECM T-Level=0.19 ~= -16-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

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