M1108463 Mersenne number exponent details

Residue

Status

L-L

CD5216B21D47758D

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	26.8064	68.6567%	300000	10000000	0.0356	4.1189%	26.8420	69.9477%	1.2910%
PrimeNet	2⁵⁶	0.0087	62.5000%	4500	65000	0.0003	2.0309%	0.0090	63.2616%	0.7616%
GPU72	2⁶⁰	0.1386	65.0000%	4500	22000	0.0002	0.6850%	0.1388	65.2398%	0.2398%
Difference	+7	+26.6679	+3.6567%	+295500	+9978000	+0.0354	+3.4338%	+26.7032	+4.7079%	+4.7079%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

26.8064

68.6567%

300000

10000000

0.0356

4.1189%

26.8420

69.9477%

1.2910%

PrimeNet

2⁵⁶

0.0087

62.5000%

4500

65000

0.0003

2.0309%

0.0090

63.2616%

0.7616%

GPU72

2⁶⁰

0.1386

65.0000%

4500

22000

0.0002

0.6850%

0.1388

65.2398%

0.2398%

Difference

+26.6679

+3.6567%

+295500

+9978000

+0.0354

+3.4338%

+26.7032

+4.7079%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1108463	241440385105176533047	21	67.710	108907733097621 3² × 12100859233069	2009-04-11	9	12100859233069	29.030	28,334	52,920

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

1108463

241440385105176533047

67.710

108907733097621
3² × 12100859233069

2009-04-11

12100859233069

29.030

28,334

52,920

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2002-03-03T00:00:00	Jocelyn Larouche	v4_computers	15000	165000		-		-	-	0.001	-	-	0.700%
2016-03-17T18:59:57	alpertron	Manual testing	300000	10000000	12	-		-	-	0.036	-	-	4.119%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2001-12-01T00:00:00	ANONYMOUS	v4_computers	2¹	2⁵⁷		-	-	0.017	-	-
2022-03-07T17:30:51	LordJulius	Manual testing	2⁵⁷	2⁶⁰		-	-	0.121	-	-
2009-02-18T02:49:00	Sturle Sunde	gopher.ifi	2⁶⁰	2⁶¹		-	-	0.139	-	-
2022-04-12T17:43:16	LordJulius	Manual testing	2¹	2⁶¹		-	-	0.277	-	-
2022-04-12T17:43:16	LordJulius	Manual testing	2⁶¹	2⁶²		-	-	0.277	-	-
2022-04-12T17:43:16	LordJulius	Manual testing	2⁶²	2⁶³		-	-	0.886	-	-
2022-04-12T17:43:16	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	1.771	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:	17.548 GHz-days
Estimated T-Level:	25.344

Digits	B1	Curves	Complete	FacMiss
20	11000	322 / 100	3.220	3.931%
25	50000	322 / 280	1.150	31.599%
30	250000	44 / 640	0.069	93.351%

New Calculation Method

Total ECM effort:	17.548 GHz-days
Estimated T-Level:	25.344

Digits	B1	Complete	FacMiss
20	11000	12.634	0.000%
25	50000	1.341	26.168%
30	250000	0.107	89.841%
35	1000000	0.007	99.298%

ECM Summary

B1	B2	factor	curves	GHz-days
		241440385105176533047	1	0.00000e+0
50000	5000000		278	9.80
250000	25000000		44	7.752

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2007-10-04T04:29:00	Chad Davis	Bayes	50000	5000000						1	0.035
2008-04-24T09:46:00	Scott Kurowski	LM-Dell4600	50000	5000000						3	0.106
2008-12-14T01:17:00	Sturle Sunde	v23	50000	5000000						3	0.106
2009-04-11T05:14:00	Chang Chia-Tche	euler06			241440385105176533047	67.710		1		1	-
2017-04-28T21:38:56	TJAOI	Manual testing	50000	5000000						130	4.581
2018-04-20T14:10:54	TJAOI	Manual testing	50000	5000000						141	4.968
2020-06-01T14:16:18	TJAOI	Manual testing	250000	25000000						44	7.752

date	userid	compid	res64	spent (GHz-days)
2002-04-20T00:00:00	ANONYMOUS	v4_computers	CD5216B21D47758D	0.033

date

userid

compid

res64

spent (GHz-days)

2002-04-20T00:00:00

ANONYMOUS

v4_computers

CD5216B21D47758D

0.033

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-29T02:37:25

Oliver Kruse

GTX-3

241440385105176533047

219625E93C5E1A__

2017-10-16T15:25:15

Oliver Kruse

Threadripper

241440385105176533047

219625E93C5E1A__

2018-01-02T09:04:19

ATH

ec2-1xf

241440385105176533047

219625E93C5E1A__

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 = 300000, B2 = 10000000 (P-1 stage 2)

B1 = 300000 (P-1 stage 1)

B1 = 15000, B2 = 165000 (P-1 stage 2)

B1 = 15000 (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

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