M1546291 Mersenne number exponent details

≡

M1546291

<<<

>>>

is 2 ^1546291 - 1

has 465480 decimal digits

takes 0.069 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

-unknown- primality 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	19.2163	68.6567%	500000	15000000	0.0835	4.9666%	19.2998	70.2134%	1.5567%
PrimeNet	2⁵⁷	0.0124	63.1579%	6500	110000	0.0008	2.4193%	0.0132	64.0492%	0.8913%
GPU72	2⁶¹	0.1987	65.5738%	6500	60000	0.0006	1.0484%	0.1993	65.9347%	0.3609%
Difference	+6	+19.0176	+3.0829%	+493500	+14940000	+0.0829	+3.9182%	+19.1005	+4.2787%	+4.2787%

Known prime factors (4 factors, 222.9 bits, 0.01441688% known):

Remaining cofactor is not a probable-prime

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
1546291	25310758028791	14	44.525	8184345 3 × 5 × 13 × 19 × 47²	-	2209	2209	2.278e-6	0.0001	0.0003
1546291	208263196053823	15	47.565	67342821 3 × 7 × 13 × 19 × 12983	2008-08-26	19	12983	1.659e-5	4.698e-5	8.556e-5
1546291	235205581048100321	18	57.707	76054759760 2⁴ × 5 × 7 × 135812071	2015-07-21	16	135812071	0.0150	0.4792	0.8951
1546291	10334980021476031698977	23	73.130	3341861273678768 2⁴ × 131 × 227 × 7023786179	2017-12-01	227	7023786179	1,689.1	24.785	46.291

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1546291	25310758028791 208263196053823	5271299361620974605419617993	28	92.090
1546291	25310758028791 235205581048100321	5953231548929657468509174341911	31	102.232
1546291	208263196053823 235205581048100321	48984666038773872568837819577183	32	105.272
1546291	25310758028791 10334980021476031698977	261586178555969050931452123211246807	36	117.655
1546291	208263196053823 10334980021476031698977	2152395970425006628722164404626039071	37	120.695
1546291	235205581048100321 10334980021476031698977	2430844981071778369893886409163969071617	40	130.837
1546291	25310758028791 208263196053823 235205581048100321	1239839029228541625235030957695150898160675753	46	149.797
1546291	25310758028791 208263196053823 10334980021476031698977	54478773589572132312488918329243590798214108893161	50	165.220
1546291	25310758028791 235205581048100321 10334980021476031698977	61526529121408820800056215629453087097422389226925 047	53	175.361
1546291	208263196053823 235205581048100321 10334980021476031698977	50625554486940343813399729163625053510054161527364 1791	54	178.402
1546291	25310758028791 208263196053823 235205581048100321 10334980021476031698977	12813711596923215419312571408576477344799603649199 944796030998804681	68	222.927

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:28:40	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 25310758028791 skipped known factor: 208263196053823	-	-	0.084	-	-	4.967%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2008-08-26T20:19:00	ANONYMOUS	Manual testing	?	?	208263196053823	47.565	15	4.46421e-6	0.153	9.87024e-6
2015-07-10T10:12:00	TJAOI	Manual testing	2⁵⁷	2⁵⁸*	235205581048100321	57.707	18	0.003	0.140	0.005

ECM factoring results:

Old Calculation Method

Total ECM effort:	14.025 GHz-days
Estimated T-Level:	24.482

Digits	B1	Curves	Complete	FacMiss
20	11000	251 / 100	2.510	8.025%
25	50000	251 / 280	0.896	40.737%

New Calculation Method

Total ECM effort:	14.025 GHz-days
Estimated T-Level:	24.482

Digits	B1	Complete	FacMiss
20	11000	9.654	0.006%
25	50000	0.893	40.933%
30	250000	0.056	94.522%
35	1000000	0.003	99.737%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		250	13.97
50000	5000000	10334980021476031698977	1	0.056

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-12-01T07:43:05	ATH	ec2-1xe	50000	5000000	10334980021476031698977	73.130	1	2		1	0.056
2017-12-26T10:09:41	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2019-01-01T14:41:46	Chang Chia-Tche	exbpc13	50000	5000000						3	0.168
2019-07-19T09:16:12	TJAOI	Manual testing	50000	5000000						244	13.63

Lucas-Lehmer results:
No L-L results for M1546291

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-10-01T17:52:02

Oliver Kruse

GTX-0

25310758028791

208263196053823

235205581048100321

5BA7DC7DBA279664

2017-10-05T21:04:59

Oliver Kruse

Manual testing

25310758028791

208263196053823

235205581048100321

5BA7DC7DBA2796__

2017-11-10T16:07:46

kkmrkkblmbrbk

c4.xlarge

25310758028791

208263196053823

235205581048100321

5BA7DC7DBA2796__

2017-12-01T23:25:48

kkmrkkblmbrbk

c4.xlarge

25310758028791

208263196053823

235205581048100321

10334980021476031698977

0FFCCCC0CC8692__

2017-12-02T17:36:47

Oliver Kruse

GTX-0

25310758028791

208263196053823

235205581048100321

10334980021476031698977

0FFCCCC0CC8692__

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 = 500000, B2 = 15000000 (P-1 stage 2)

B1 = 500000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

TF factor-bounds graph:

2⁶⁷

2⁵⁸

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2019-07-19T09:16:12+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