M1 105 519 Mersenne number exponent details

is 2 ^1105519 - 1

has 332795 decimal digits

takes 0.033 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	432.4469	70.4225%	15000000	54022094280	127.1008	13.8343%	559.5477	74.5144%
Target	2⁶⁰	0.1389	65.0000%	4500	176000	0.0006	0.6846%	0.1395	65.2396%
Difference	+11	+432.3080	+5.4225%	+14995500	+54021918280	+127.1002	+13.1498%	+559.4082	+9.2748%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1105519	2915595290210483905698188678755302313032196817	46	151.031	1318654537014055798994946572042317822232 2³ × 7 × 73 × 191 × 29641 × 681419 × 6274553 × 12150571 × 1096731227	2023-04-06	12150571	1096731227	1.633e+11	3.0617	4.7962

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	Jocelyn Larouche	v4_computers	15000	153750		-		-	-	0.001	-	-	0.355%
2012-09-25	kurly	smile	500000	10000000		-		-	-	0.044	-	-	2.938%
2015-02-21	mikr	MSI	5000000	200000000		-		-	-	0.671	-	-	6.610%
2018-11-20	Jocelyn Larouche	Manual testing	1105519	222209319	12	-		-	-	0.565	-	-	5.696%
2022-10-10	Numberwang	colab	118000	5258424600		-		-	-	12.32	-	-	5.607%
2022-11-24	Jocelyn Larouche	Manual testing	1105519	8063441100		-		-	-	18.93	-	-	8.841%
2023-04-06	mikr	MSI	15000000	54022094280			2915595290210483905698188678755302313032196817	46	151.031	127.1	0.066	254.2	13.834%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2016-02-23	Mark Rose	Manual testing	2⁵⁷	2⁶⁰		-	-	0.122	-	-
2009-02-14	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.139	-	-
2011-05-09	Xyzzy	Manual testing	2⁶¹	2⁶²		-	-	0.278	-	-
2012-10-07	dbaugh	Manual testing	2⁶²	2⁶³		-	-	0.888	-	-
2014-12-22	Matthias Wurtinger	Manual testing	2⁶³	2⁶⁴		-	-	1.776	-	-
2014-12-28	Matthias Wurtinger	Manual testing	2⁶⁴	2⁶⁵		-	-	3.380	-	-
2015-05-25	omylist	Manual testing	2⁶⁵	2⁶⁶		-	-	6.759	-	-
2015-12-06	ramgeis	Manual testing	2⁶⁶	2⁶⁷		-	-	13.52	-	-
2015-12-06	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	27.04	-	-
2015-12-06	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	54.08	-	-
2015-12-06	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	108.2	-	-
2015-12-06	ramgeis	Manual testing	2⁷⁰	2⁷¹		-	-	216.3	-	-

ECM factoring results:

Total ECM effort:	17.682 GHz-days
Estimated T-Level:	25.656

Digits	B1	Complete	FacMiss
20	11000	14.948	0.000%
25	50000	1.627	19.652%
30	250000	0.131	87.696%
35	1000000	0.009	99.136%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		287	10.11
250000	25000000		43	7.573

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-02	Chad Davis	Bayes	50000	5000000						1	0.035
2008-04-24	paulie	iMac3.4	50000	5000000						3	0.106
2008-12-13	Sturle Sunde	v23	50000	5000000						3	0.106
2009-04-23	James Hintz	02_060209	50000	5000000						3	0.106
2009-09-01	Lupo	yorick	50000	5000000						3	0.106
2009-11-28	Geoff Wing	GW1	50000	5000000						3	0.106
2010-04-27	maxybo	CB418E216	50000	5000000						3	0.106
2011-01-03	Boots	rchok28bo	50000	5000000						3	0.106
2011-10-16	Bruce	dell-gx260	50000	5000000						3	0.106
2012-03-23	Pool Party	sts	50000	5000000						3	0.106
2012-09-04	OS1	Tina	50000	5000000						3	0.106
2013-03-20	Pool Party	sts	50000	5000000						3	0.106
2013-08-05	Pool Party	sts	50000	5000000						3	0.106
2013-10-22	561	561	50000	5000000						3	0.106
2014-03-14	mikr	MSI	50000	5000000						20	0.704
2016-03-22	Bruce	Desk9	50000	5000000						3	0.106
2016-05-17	raman22feb1988	Gokul_Nath	50000	5000000						3	0.106
2016-06-22	raman22feb1988	Nithya	50000	5000000						3	0.106
2016-06-25	raman22feb1988	Ashok	50000	5000000						3	0.106
2016-08-30	Bruce	Desk9	50000	5000000						3	0.106
2016-12-23	OS1	Tina	50000	5000000						3	0.106
2017-04-16	driveByUpgrades	AMD8	50000	5000000						3	0.106
2017-06-09	TJAOI	Manual testing	50000	5000000						62	2.184
2018-03-16	Agusss	vero_pc	50000	5000000						3	0.106
2018-04-20	TJAOI	Manual testing	50000	5000000						138	4.861
2018-06-04	arnaud	ATTAX04	50000	5000000						3	0.106
2020-04-27	TJAOI	Manual testing	250000	25000000						43	7.573

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1997-01-01	John Hocking		ABEDBA6E6B0FC5B9	0.033
2002-04-20	ANONYMOUS	v4_computers	ABEDBA6E6B0FC5B9	0.033
2016-06-01	MadPoo	Manual testing	ABEDBA6E6B0FC5B9	0.033

PRP results:

date

userid

compid

cofactors

res64

PRP

2020-11-05

Ethan O'Connor

Highland2020

3D1549C7ED0EED1A

2023-04-06

mikr

Nitron

2915595290210483905698188678755302313032196817

3D1549C7ED0EED1A

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 = 15000000, B2 = 54022094280 (P-1 stage 2)

B1 = 1105519, B2 = 8063441100 (P-1 stage 2)

B1 = 118000, B2 = 5258424600 (P-1 stage 2)

B1 = 5000000, B2 = 200000000 (P-1 stage 2)

B1 = 15000000 (P-1 stage 1)

B1 = 1105519, B2 = 222209319 (P-1 stage 2)

B1 = 5000000 (P-1 stage 1)

B1 = 1105519 (P-1 stage 1)

B1 = 500000, B2 = 10000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

B1 = 118000 (P-1 stage 1)

B1 = 15000, B2 = 153750 (P-1 stage 2)

B1 = 15000 (P-1 stage 1)

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

TF factor-bounds graph:

2⁷¹

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

2⁶⁶

2⁶⁵

2⁶⁴

2⁶³

2⁶²

2⁶¹

2⁶⁰

2⁵⁷

this exponent TF target: 60

TF double-checked to: 67.9

ECM T-Level=25.66 ~= 69-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