13 163 Exponent Status

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

PrimeNet Exponent Status

M_n

Details

Composite, with 3 known prime factors. Cofactor is composite.

Trial Factored to 2⁶⁸

TF target 2⁴⁴

Factored

Factor	Digits	Bits	Date
737129	6	19.5	old
4101948096473	13	41.9	2008-08-26 19:58:40
837579573618384416431	21	69.5	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	1329A41EB0A04A69	3	0	1	3
Verified	No proof (small exponent)	2017-10-02	kkmrkkblmbrbk	1329A41EB0A04A69	3	0	1	3
Verified	No proof (small exponent)	2017-12-07	ATH	1329A41EB0A04A69	3	9382	1	3
Verified	No proof (small exponent)	2020-04-17	Oliver Kruse	FEC31C08C4DF8B95	3	7086	5	3
Verified	No proof (small exponent)	2024-07-01	kkmrkkblmbrbk	FEC31C08C4DF8B95	3	825	5	3

History

Date	User	Type	Result
2025-02-28	masser	NF-PP1	Start=178/23, B1=430000000, B2=429570000000
2025-02-01	masser	NF-PP1	Start=2/7, B1=430000000, B2=429570000000
2025-01-30	masser	NF-PP1	Start=6/5, B1=430000000, B2=429570000000
2024-07-01	kkmrkkblmbrbk	C-PRP	M13163/4101948096473/737129/837579573618384416431 : FEC31C08C4DF8B95
2023-10-10	-anonymous-	F-PM1	Factor: 837579573618384416431 / 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	M13163/737129/4101948096473/837579573618384416431 : FEC31C08C4DF8B95
2017-12-07	ATH	C-PRP	M13163/737129/4101948096473/837579573618384416431 : 1329A41EB0A04A69
2017-10-02	kkmrkkblmbrbk	C-PRP	M13163/737129/4101948096473/837579573618384416431 : 1329A41EB0A04A69
2017-09-21	Oliver Kruse	C-PRP	M13163/737129/4101948096473/837579573618384416431 : 1329A41EB0A04A69
2008-08-29	-anonymous-	F-ECM	Factor: 837579573618384416431
2008-08-26	-anonymous-	F	Factor: 4101948096473