M102719861 Mersenne number exponent details

≡

is 2 ^102719861 - 1

has 30921760 decimal digits

takes 408.989 GHz-days to do one PRP test

Last-known PrimeNet details:
-unknown- L-L tests remaining

	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	2⁶⁷	0.2893	59.7015%	-	-	-	-	0.2893	59.7015%	-2.7985%
PrimeNet	2⁷²	9.3101	62.5000%	450000	22000000	9.3765	5.3819%	18.6866	67.8819%	5.3819%
GPU72	2⁷⁶	148.9877	64.4737%	650000	22000000	10.4682	3.8530%	159.4559	68.3267%	3.8530%
Difference	-9	-148.6984	-4.7722%	-650000	-22000000	-10.4682	-3.8530%	-159.1666	-8.6252%	-8.6252%

Known prime factors (3 factors, 109.9 bits, 0.00010703% known):

Remaining cofactor is PRP status unknown

								GHz-days
exponent	factor	digits	bits*	k	min B1	min B2	date found	min. TF	min. P-1	normal P-1
102719861	616319167	9	29.199	3 3	1	3	2007-09-18	6.967e-13	6.402e-6	1.175e-5
102719861	266249879713	12	37.954	1296 2⁴ × 3⁴	81	81	2007-09-18	2.282e-10	0.0005	0.0010
102719861	7596339160673	13	42.788	36976 2⁴ × 2311	16	2311	2007-09-18	5.724e-9	0.0008	0.0014

4 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
102719861	616319167 266249879713	164094904078566359071	21	67.153
102719861	616319167 7596339160673	4681769423755462519391	22	71.988
102719861	266249879713 7596339160673	2022524387788337630126849	25	80.742
102719861	616319167 266249879713 7596339160673	1246520545918893220514533680014783	34	109.942

P-1 results:
Exponent "102719861" not found

Trial Factoring results:
Exponent "102719861" not found

ECM factoring results:
Exponent "102719861" not found

Lucas-Lehmer results:
Exponent "102719861" not found

PRP results:
Exponent "102719861" not found

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

10⁰

10¹

10²

10⁰

10¹

10²

10³

10⁴

TF factor-bounds graph:

2⁶⁷

2²⁰

2³⁰

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2007-09-18T05:13:39+00:00