M1825261 Mersenne number exponent details

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M1825261

<<<

>>>

is 2 ^1825261 - 1

has 549459 decimal digits

takes 0.099 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	16.2793	68.6567%	500000	15000000	0.1015	5.0670%	16.3807	70.2449%	1.5882%
PrimeNet	2⁵⁷	0.0105	63.1579%	8000	150000	0.0012	2.8777%	0.0118	64.2181%	1.0602%
GPU72	2⁶¹	0.1683	65.5738%	9000	140000	0.0013	1.5938%	0.1696	66.1224%	0.5487%
Difference	+6	+16.1110	+3.0829%	+491000	+14860000	+0.1002	+3.4732%	+16.2112	+4.1224%	+4.1224%

Known prime factors (4 factors, 231.8 bits, 0.01269924% 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
1825261	75160418582423	14	46.095	20588951 19 × 101 × 10729	-	101	10729	7.616e-6	5.349e-5	8.585e-5
1825261	21560226597042457	17	54.259	5906066748 2² × 3 × 492172229	2014-11-13	4	492172229	0.0019	2.1093	3.9396
1825261	2495090174988113239	19	61.114	683488601079 3 × 29 × 7856190817	2016-04-01	29	7856190817	0.2768	33.670	62.886
1825261	1480071051875813114303	22	70.326	405440934714491 13 × 23 × 1355989748209	2019-10-18	23	1355989748209	226.51	5,811.4	10,854

11 Composite Factors:

exponent	prime factors	composite factor	digits	bits*
1825261	75160418582423 21560226597042457	1620475655765600487196284933311	31	100.354
1825261	75160418582423 2495090174988113239	187532021952997641061675778998097	33	107.209
1825261	21560226597042457 2495090174988113239	53794709552798037257895088006788223	35	115.373
1825261	75160418582423 1480071051875813114303	111242759790713220007561960125696169	36	116.421
1825261	21560226597042457 1480071051875813114303	31910667258165512024646433114284962471	38	124.585
1825261	2495090174988113239 1480071051875813114303	3692910739819663370776900880854614557417	40	131.440
1825261	75160418582423 21560226597042457 2495090174988113239	4043232887508169671752259868592020520334831204329	49	161.468
1825261	75160418582423 21560226597042457 1480071051875813114303	23984191083681403534589842250093490641558635752472 33	52	170.680
1825261	75160418582423 2495090174988113239 1480071051875813114303	27756071699237129538486865434759596909433389468048 1391	54	177.535
1825261	21560226597042457 2495090174988113239 1480071051875813114303	79619992353163643101491334372367463751703831390213 253569	56	185.699
1825261	75160418582423 21560226597042457 2495090174988113239 1480071051875813114303	59842719527930978442175336209047936643352835201485 49837168205625417687	70	231.794

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2016-03-16T12:38:44	alpertron	Manual testing	500000	15000000	12	-	skipped known factor: 75160418582423	-	-	0.101	-	-	5.067%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2014-11-13T12:15:00	TJAOI	Manual testing	2⁵⁴	2⁵⁵*	21560226597042457	54.259	17	0.001	0.209	0.001
2016-04-01T11:52:09	TJAOI	Manual testing	2⁶¹	2⁶²*	2495090174988113239	61.114	19	0.109	0.201	0.221

ECM factoring results:

Old Calculation Method

Total ECM effort:	20.275 GHz-days
Estimated T-Level:	24.732

Digits	B1	Curves	Complete	FacMiss
20	11000	265 / 100	2.650	6.972%
25	50000	265 / 280	0.946	38.747%

New Calculation Method

Total ECM effort:	20.275 GHz-days
Estimated T-Level:	24.732

Digits	B1	Complete	FacMiss
20	11000	9.049	0.012%
25	50000	0.820	44.054%
30	250000	0.051	95.055%
35	1000000	0.002	99.767%

ECM Summary

B1	B2	factor	curves	GHz-days
50000	5000000		37	2.555
50000	5000000	1480071051875813114303	3	0.207
50000	6600000		225	17.51

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2017-08-12T15:27:53	Richard B. Woods	Puttputt	50000	5000000						1	0.069
2018-04-04T20:31:11	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2019-10-18T23:19:19	Chang Chia-Tche	exbpc13	50000	5000000	1480071051875813114303	70.326	3	2		3	0.207
2020-05-07T14:02:54	Greg Hogan	azure2	50000	5000000						3	0.207
2020-06-15T13:15:56	Chang Chia-Tche	exbpc13	50000	5000000						3	0.207
2020-07-11T09:08:45	kracker	O0	50000	5000000						3	0.207
2020-08-13T21:16:06	volki	home	50000	5000000						3	0.207
2020-10-16T12:40:19	nordi	sweet16	50000	5000000						7	0.483
2020-12-30T08:38:48	_p95holder_	TFL1_PRPt8pE_n	50000	5000000						7	0.483
2021-03-28T08:50:54	_p95holder_	TFL18_PRPt12pE_m	50000	5000000						7	0.483
2021-04-02T11:39:59	TJAOI	Manual testing	50000	6600000						225	17.51

Lucas-Lehmer results:
No L-L results for M1825261

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-30T15:34:58

alpertron

Manual testing

75160418582423

21560226597042457

2495090174988113239

F6252D1E958223__

2017-10-19T23:57:57

Oliver Kruse

Threadripper

75160418582423

21560226597042457

2495090174988113239

F6252D1E958223__

2019-10-19T19:44:51

mnd9

27016b

75160418582423

21560226597042457

2495090174988113239

1480071051875813114303

D709AB8C5357A9C1

2019-10-19T20:13:28

ATH

ec2-PRPCFDC

75160418582423

21560226597042457

2495090174988113239

1480071051875813114303

D709AB8C5357A9C1

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

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶²

2⁵⁵

2⁴⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

Last modified: 2021-04-02T11:39:59+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