M22 411 801 Mersenne number exponent details

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is 2 ^22411801 - 1

has 6746625 decimal digits

takes 16.342 GHz-days to do one PRP test

Last-known PrimeNet details:

Exponent is not assigned to anyone

factored, 0 LL tests remaining

	Residue	Status
L-L	509ED65FBE08D0AB	double-checked
PRP	-unknown-	-unknown-

	Trial Factoring			P-1 Factoring				Combined
	Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability
Actual	2⁷⁰	10.6618	64.2857%	350000	7000000	0.7531	4.2411%	11.4149	65.8004%
Target	2⁶⁹	5.3270	63.7681%	170000	40000000	2.4741	3.9770%	7.8011	65.2091%
Difference	+1	+5.3349	+0.5176%	+180000	-33000000	-1.7210	+0.2641%	+3.6139	+0.5913%

Known prime factors (1 factor, 89.8 bits, 0.00040047% known):

Remaining cofactor is PRP status unknown

						P-1		GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
22411801	1043187363347975865450924439	28	89.753	23273171204491238019 3 × 11² × 19² × 821² × 1153 × 228521	2017-12-09	674041	674041	6,513,022	0.7127	1.4504

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2004-07-13	ANONYMOUS	v4_computers	325000	325000		-		-	-	0.344	-	-	1.695%
2017-12-09	Tha	Manual testing	350000	7000000	12		1043187363347975865450924439	28	89.753	0.753	32.68	1.506	4.241%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
2003-03-16	ANONYMOUS	v4_computers	2¹	2⁶⁷		-	-	1.326	-	-
2017-05-04	ramgeis	Manual testing	2⁶⁷	2⁶⁸		-	-	1.334	-	-
2017-05-15	ramgeis	Manual testing	2⁶⁸	2⁶⁹		-	-	2.667	-	-
2017-05-15	ramgeis	Manual testing	2⁶⁹	2⁷⁰		-	-	5.335	-	-

ECM factoring results:
No ECM results for M22411801

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
2004-08-06	ANONYMOUS	v4_computers	509ED65FBE08D0AB	16.34
2009-10-02	shaneamy	v4_computers	509ED65FBE08D0AB	16.34
2009-10-25	shaneamy	v4_computers	509ED65FBE08D0AB	16.34

PRP results:
No PRP results for M22411801

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 = 350000, B2 = 7000000 (P-1 stage 2)

B1 = 350000 (P-1 stage 1)

B1 = 325000 (P-1 stage 1)

10⁴

10⁵

10⁶

10⁴

10⁵

10⁶

10⁷

TF factor-bounds graph:

2⁷⁰

2⁶⁹

2⁶⁸

2⁶⁷

this exponent TF target: 69

TF double-checked to: 67.9

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

Last modified: 2023-06-05T21:50:05+00:00