M1 710 619 Mersenne number exponent details

is 2 ^1710619 - 1

has 514948 decimal digits

takes 0.081 GHz-days to do one PRP test

Exponent is not assigned to anyone

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷¹	279.4768	70.4225%	17000000	256271815800	953.8995	16.2831%	1,233.3763	75.2387%
Target	2⁶¹	0.1796	65.5738%	7000	800000	0.0034	1.3030%	0.1830	66.0224%
Difference	+10	+279.2972	+4.8488%	+16993000	+256271015800	+953.8961	+14.9801%	+1,233.1933	+9.2163%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1710619	1689246413256159497216856379896984918513307241	46	150.243	493752966983343309415146324195213813980 2² × 5 × 109 × 1823 × 45439 × 278827 × 3674689 × 5044577 × 529002373	2023-06-16	5044577	529002373	8.691e+10	2.2923	3.6734

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2011-02-08	Carsten Kossendey	leela	90000	1507500		-		-	-	0.011	-	-	1.430%
2014-04-01	Jocelyn Larouche	Manual testing	100000	100000		-		-	-	0.007	-	-	0.495%
2014-05-01	Aaron Haviland	Manual testing	1500000	27500000		-		-	-	0.199	-	-	4.374%
2018-02-04	Jocelyn Larouche	low 4M	1500000	1500000		-		-	-	0.102	-	-	1.975%
2018-02-10	Jocelyn Larouche	low 4M	1710619	27500000	12	-		-	-	0.213	-	-	4.432%
2018-02-11	Jocelyn Larouche	low 4M	1710619	55000000	12	-		-	-	0.315	-	-	5.044%
2018-02-27	Jocelyn Larouche	low 4M	1710619	110000000	12	-		-	-	0.519	-	-	5.666%
2018-04-08	Jocelyn Larouche	low 4M	1710619	171061900	12	-		-	-	0.746	-	-	6.068%
2018-10-16	Jocelyn Larouche	low 4M	1710619	188168090	12	-		-	-	0.810	-	-	6.156%
2023-01-03	Jocelyn Larouche	Manual testing	1710619	1252445040		-		-	-	4.767	-	-	7.939%
2023-03-18	Jocelyn Larouche	Manual testing	1710619	3510509730		-		-	-	13.16	-	-	8.939%
2023-06-15	linament	U2K	17000000	17000000		-		-	-	1.160	-	-	4.380%
2023-06-16	linament	Cyber	17000000	256271815800			1689246413256159497216856379896984918513307241	46	150.243	953.9	0.161	1,908	16.283%

P+1 Factoring results:

date	userid	compid	b1	b2	start		factor	Smooth	digits	bits*	ghz-days
2021-05-09	Carlos Pinho	HomeComputer	1000000	51000000	2	7			-	-	0.286
2021-05-31	LaurV	butu	5000000	365000000	2	7			-	-	1.830

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-02-02	ANONYMOUS	v4_computers	2¹	2⁵⁸		-	-	0.022	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁸	2⁶⁰		-	-	0.067	-	-
2010-04-21	Architects Cubed	a3_bu2	2⁶⁰	2⁶¹		-	-	0.090	-	-
2016-02-23	Mark Rose	Manual testing	2⁶¹	2⁶²		-	-	0.180	-	-
2010-10-16	GrunwalderGIMP	Manual testing	2¹	2⁶³		-	-	0.933	-	-
2016-02-23	Mark Rose	Manual testing	2⁶²	2⁶³		-	-	0.574	-	-
2013-08-14	BloodIce	Manual testing	2⁶³	2⁶⁴		-	-	1.148	-	-
2013-11-12	David Campeau	Manual testing	2⁶⁴	2⁶⁵		-	-	2.184	-	-
2014-01-18	Never Odd Or Even	Manual testing	2⁶⁵	2⁶⁶		-	-	4.368	-	-
2014-01-18	Never Odd Or Even	Manual testing	2⁶⁶	2⁶⁷		-	-	8.737	-	-
2014-01-18	Never Odd Or Even	Manual testing	2⁶⁷	2⁶⁸		-	-	17.47	-	-
2014-01-18	Never Odd Or Even	Manual testing	2⁶⁸	2⁶⁹		-	-	34.95	-	-
2014-01-18	Never Odd Or Even	Manual testing	2⁶⁹	2⁷⁰		-	-	69.90	-	-
2015-11-11	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	139.8	-	-

ECM factoring results:

Total ECM effort:	43.269 GHz-days
Estimated T-Level:	25.602

Digits	B1	Complete	FacMiss
20	11000	13.567	0.000%
25	50000	1.489	22.553%
30	250000	0.120	88.662%
35	1000000	0.008	99.200%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		278	16.54
250000	209815174		23	26.73

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2008-06-28	Team_Bundu	bundu4	50000	5000000						3	0.178
2009-06-19	Lupo	yorick	50000	5000000						3	0.178
2010-07-15	SubPrime	abd0	50000	5000000						3	0.178
2011-11-25	Dmitry B. Khachaturov	dix-home	50000	5000000						3	0.178
2013-04-23	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-01-13	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2014-10-11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-06-11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2015-09-08	mikr	MSI	50000	5000000						12	0.714
2016-09-11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.178
2016-11-14	Bruce	DESK3	50000	5000000						3	0.178
2017-01-08	Bruce	DESK3	50000	5000000						3	0.178
2017-04-26	ANONYMOUS	Worker	50000	5000000						3	0.178
2017-11-19	Bruce	DESK3	50000	5000000						3	0.178
2018-01-24	Bruce	DESK3	50000	5000000						3	0.178
2019-04-01	nordi	nordiputer	50000	5000000						50	2.974
2020-01-09	Keysarecool	Boat_Anchor	50000	5000000						3	0.178
2020-01-23	EricP	Cannonfodder	50000	5000000						3	0.178
2020-01-23	Sebastian Hornbostel	NZXT	50000	5000000						3	0.178
2020-01-30	EricP	Cannonfodder	50000	5000000						3	0.178
2020-02-09	Yuji HASEGAWA	sx1w7	50000	5000000						3	0.178
2020-02-16	IanGlencross	glenx24	50000	5000000						3	0.178
2020-02-23	mnd9	office2	50000	5000000						3	0.178
2020-03-01	IanGlencross	glenx24	50000	5000000						3	0.178
2020-03-07	Alvin Bunk	BADCAT	50000	5000000						3	0.178
2020-03-15	mnd9	office2	50000	5000000						3	0.178
2020-03-16	TJAOI	Manual testing	50000	5000000						144	8.565
2023-03-07	TJAOI	Manual testing	250000	209815174						23	26.73

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	sean peters		163AF41646AB4C3A	0.081
1999-02-21	ANONYMOUS	v4_computers	163AF41646AB4C3A	0.081
2015-07-04	MadPoo	Manual testing	163AF41646AB4C3A	0.081

PRP results:

date

userid

compid

cofactors

res64

PRP

2023-06-16

linament

Cyber

1689246413256159497216856379896984918513307241

7AED78A94F5A5E05

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 = 17000000, B2 = 256271815800 (P-1 stage 2)

B1 = 1710619, B2 = 3510509730 (P-1 stage 2)

B1 = 1710619, B2 = 1252445040 (P-1 stage 2)

B1 = 17000000 (P-1 stage 1)

B1 = 1710619, B2 = 188168090 (P-1 stage 2)

B1 = 1710619, B2 = 171061900 (P-1 stage 2)

B1 = 1710619, B2 = 110000000 (P-1 stage 2)

B1 = 1710619, B2 = 55000000 (P-1 stage 2)

B1 = 1710619, B2 = 27500000 (P-1 stage 2)

B1 = 1500000, B2 = 27500000 (P-1 stage 2)

B1 = 1710619 (P-1 stage 1)

B1 = 1500000 (P-1 stage 1)

B1 = 90000, B2 = 1507500 (P-1 stage 2)

B1 = 100000 (P-1 stage 1)

B1 = 90000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁸

this exponent TF target: 61

TF double-checked to: 67.9

ECM T-Level=25.6 ~= 68-bit

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

2¹¹⁰

2¹²⁰

2¹³⁰

2¹⁴⁰

2¹⁵⁰

2¹⁶⁰

Last modified: 2023-07-11T14:45:05+00:00

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