13 093 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 2 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
3231981325161647	16	51.5	old
343107337692217790195130191	27	88.1	2008-08-29 02:24:32

P-1 factors

Date	Factors	B1	B2
2023-10-10	No new factors discovered	100000000000	122154521813133808

ECM

Digits	B1	Curves
25	50000	280 / 280
30	250000	640 / 640
35	1000000	1566 / 1566
40	3000000	4588 / 4588
45	11000000	1581 / 9201

Estimated T-Level: 40.9 ⓘ

TF below 2^131 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	4425F181BC4AB2F5	2	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	4425F181BC4AB2F5	2	0	1	3
Verified	No proof (small exponent)	2017-12-07	ATH	4425F181BC4AB2F5	2	4041	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	DFCBE9A7F46EB97E	2	6705	5	3
Verified	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	DFCBE9A7F46EB97E	2	2825	5	3

History

Date	User	Type	Result
2025-03-01	masser	NF-PP1	Start=141/11, B1=430000000, B2=429570000000
2025-01-31	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2025-01-31	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M13093/3231981325161647/343107337692217790195130191 : DFCBE9A7F46EB97E
2023-10-10	-anonymous-	F-PM1	Factor: 343107337692217790195130191 / B1=100000000000, B2=122154521813133810
2023-05-17	JacobZ	NF-PM1	B1=8400000000, B2=34523926202766000
2022-02-05	Joss	NF-PM1	B1=1000000, B2=3910366209750
2020-04-17	Oliver Kruse	C-PRP	M13093/3231981325161647/343107337692217790195130191 : DFCBE9A7F46EB97E
2017-12-07	ATH	C-PRP	M13093/3231981325161647/343107337692217790195130191 : 4425F181BC4AB2F5
2017-10-02	kkmrkkblmbrbk	C-PRP	M13093/3231981325161647/343107337692217790195130191 : 4425F181BC4AB2F5
2017-09-21	Oliver Kruse	C-PRP	M13093/known_factors : 4425F181BC4AB2F5
2008-08-29	-anonymous-	F-ECM	Factor: 343107337692217790195130191