4 091 Exponent Status

Great Internet Mersenne Prime Search
GIMPS
Finding World Record Primes Since 1996

PrimeNet Exponent Status

M_n

Details

Composite, with 1 known prime factor. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Assignments

Assigned	User	Work Type	Stage	% Done	Updated	Est Complete	Expired
2025-10-15	Phyxick	ECM			2025-10-15	1970-01-01

Factored

Factor	Digits	Bits	Date
1009611726327533941115754978617	31	99.7	old

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	9201 / 9201
50	44000000	16550 / 16550
55	110000000	16227 / 40830

Estimated T-Level: 52.0 ⓘ

TF below 2^168 is very unlikely to find new factors due to ECM effort.

Status	Proof	Date	User	Residue	Number of known factors	Shift	Type	Base
Verified	No proof (small exponent)	2017-09-21	Oliver Kruse	31D31D33E2A31D5E	1	0	1	3
Verified	No proof (small exponent)	2017-10-12	kkmrkkblmbrbk	31D31D33E2A31D5E	1	2246	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	3594DC9B30A128F9	1	3054	5	3
Verified	No proof (small exponent)	2024-02-03	Wentao Huang	3594DC9B30A128F9	1	1404	5	3

History

Date	User	Type	Result
2025-05-10	masser	NF-PP1	Start=191/47, B1=2600000000, B2=2597400000000
2024-02-03	Wentao Huang	C-PRP	M4091/1009611726327533941115754978617 : 3594DC9B30A128F9
2023-05-17	-anonymous-	NF-PM1	B1=79000000000, B2=797496463397964330
2020-04-17	Oliver Kruse	C-PRP	M4091/1009611726327533941115754978617 : 3594DC9B30A128F9
2017-10-12	kkmrkkblmbrbk	C-PRP	M4091/1009611726327533941115754978617 : 31D31D33E2A31D5E
2017-09-21	Oliver Kruse	C-PRP	M4091/1009611726327533941115754978617 : 31D31D33E2A31D5E
2017-09-21	Oliver Kruse	C-PRP	M4091/1009611726327533941115754978617 : 31D31D33E2A31D5E
2001-06-30	-anonymous-	NF-PM1	B1=3000000000, B2=4290000000
2001-06-17	-anonymous-	NF-PM1	B1=43000000, B2=4290000000
2001-02-11	-anonymous-	NF-PM1	B1=1000000, B2=100000000
2000-08-24	-anonymous-	NF	no factor TF: 1-56
2000-02-09	-anonymous-	NF	no factor TF: 54-55
1999-12-23	-anonymous-	NF	no factor TF: 53-54
1999-09-22	-anonymous-	NF	no factor TF: 52-53