M4479071 Mersenne number exponent details

Residue

Status

L-L

-unknown-

-unknown-

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	2⁶⁸	13.3074	66.1765%	-	-	-	-	13.3074	66.1765%	0.0000%
PrimeNet	2⁶¹	0.0686	62.2951%	19000	400000	0.0072	3.0619%	0.0758	63.4496%	1.1545%
GPU72	2⁶⁵	1.6288	64.6154%	26000	550000	0.0099	2.0893%	1.6387	65.3547%	0.7393%
Difference	+3	+11.6786	+1.5611%	-26000	-550000	-0.0099	-2.0893%	+11.6687	+0.8218%	+0.8218%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁸

13.3074

66.1765%

13.3074

66.1765%

0.0000%

PrimeNet

2⁶¹

0.0686

62.2951%

19000

400000

0.0072

3.0619%

0.0758

63.4496%

1.1545%

GPU72

2⁶⁵

1.6288

64.6154%

26000

550000

0.0099

2.0893%

1.6387

65.3547%

0.7393%

Difference

+11.6786

+1.5611%

-26000

-550000

-0.0099

-2.0893%

+11.6687

+0.8218%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4479071	8958143	7	23.095	1 1	-	1	1	2.496e-13	1.808e-7	3.681e-7
4479071	35832569	8	25.095	4 2²	2008-09-07	4	4	9.989e-13	7.234e-7	1.472e-6
4479071	85310806540972993	17	56.244	9523270176 2⁵ × 3 × 7 × 14171533	2015-08-06	32	14171533	0.0041	0.1396	0.2608
4479071	200293906342325931007	21	67.441	22358867088993 3 × 7452955696331	2022-08-03	3	7452955696331	13.268	73,434	137,155

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4479071

8958143

23.095

1
1

2.496e-13

1.808e-7

3.681e-7

4479071

35832569

25.095

4
2²

2008-09-07

9.989e-13

7.234e-7

1.472e-6

4479071

85310806540972993

56.244

9523270176
2⁵ × 3 × 7 × 14171533

2015-08-06

14171533

0.0041

0.1396

0.2608

4479071

200293906342325931007

67.441

22358867088993
3 × 7452955696331

2022-08-03

7452955696331

13.268

73,434

137,155

exponent	prime factors	composite factor	digits	bits*
4479071	8958143 35832569	320993277159367	15	48.190
4479071	8958143 85310806540972993	764226404439371430431999	24	79.338
4479071	35832569 85310806540972993	3056905361825066098809017	25	81.338
4479071	8958143 200293906342325931007	1794261455043162642568840001	28	90.535
4479071	35832569 200293906342325931007	7177045219290931543297566983	28	92.535
4479071	8958143 35832569 85310806540972993	27384195368695683097583303975431	32	104.433
4479071	8958143 35832569 200293906342325931007	64292997391874523368070296585792569	35	115.630
4479071	85310806540972993 200293906342325931007	17087234695305931082577303120368293951	38	123.684
4479071	8958143 85310806540972993 200293906342325931007	153069891875111959385872289906605389879092993	45	146.779
4479071	35832569 85310806540972993 200293906342325931007	612279516238743751625695911894512198411490119	45	148.779
4479071	8958143 35832569 85310806540972993 200293906342325931007	54848874624374886674194664532664411886145013290890 17	52	171.874

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-09-07T23:41:00	Will Edgington	Manual testing	?	?	35832569	25.095	8	8.64059e-16	1.204	1.86154e-15
2015-03-19T12:26:00	TJAOI	Manual testing	2⁵⁶	2⁵⁷*	85310806540972993	56.244	17	0.002	1.199	0.004
2022-08-04T04:11:47	J.R. Allen	Manual testing	2¹	2⁶³	35832569	25.095	8	9.98853e-13	1.204	2.15194e-12
2022-08-04T04:11:47	J.R. Allen	Manual testing	2¹	2⁶³	85310806540972993	56.244	17	0.004	1.199	0.009
2022-08-04T04:11:47	J.R. Allen	Manual testing	2¹	2⁶³	8958143	23.095	7	2.49551e-13	1.204	5.37635e-13
2022-08-04T04:11:48	J.R. Allen	Manual testing	2¹	2⁶³	8958143 35832569	48.190	15	1.64771e-5	1.204	3.54979e-5
2022-08-10T07:41:22	LordJulius	Manual testing	2¹	2⁶³	8958143 35832569	48.190	15	1.64771e-5	1.204	3.54979e-5
2022-08-10T07:41:22	LordJulius	Manual testing	2¹	2⁶³	35832569	25.095	8	9.98853e-13	1.204	2.15194e-12
2022-08-10T07:41:22	LordJulius	Manual testing	2¹	2⁶³	85310806540972993	56.244	17	0.004	1.199	0.009
2022-08-10T07:41:22	LordJulius	Manual testing	2¹	2⁶³	8958143	23.095	7	2.49551e-13	1.204	5.37635e-13
2022-08-04T14:08:17	J.R. Allen	Manual testing	2⁶³	2⁶⁴		-	-	0.438	-	-
2022-08-10T07:41:22	LordJulius	Manual testing	2⁶³	2⁶⁴		-	-	0.438	-	-
2022-08-04T14:08:17	J.R. Allen	Manual testing	2⁶⁴	2⁶⁵		-	-	0.834	-	-
2022-08-10T07:41:22	LordJulius	Manual testing	2⁶⁴	2⁶⁵		-	-	0.834	-	-
2022-08-10T07:41:22	LordJulius	Manual testing	2⁶⁵	2⁶⁶		-	-	1.668	-	-
2022-08-10T07:41:22	LordJulius	Manual testing	2⁶⁶	2⁶⁷		-	-	3.337	-	-
2022-08-03T11:20:47	TJAOI	Manual testing	2⁶⁷	2⁶⁸*	200293906342325931007	67.441	21	6.634	1.135	13.48
2022-08-10T07:41:22	LordJulius	Manual testing	2⁶⁷	2⁶⁸	200293906342325931007	67.441	21	6.634	1.135	13.48

ECM factoring results:

Old Calculation Method

Total ECM effort:	0.554 GHz-days
Estimated T-Level:	0.150

Digits	B1	Curves	Complete	FacMiss
20	11000	3 / 100	0.030	97.030%
25	50000	3 / 280	0.011	98.932%

New Calculation Method

Total ECM effort:	0.554 GHz-days
Estimated T-Level:	0.150

Digits	B1	Complete	FacMiss
20	11000	0.115	89.102%
25	50000	0.011	98.938%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		3	0.554

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