Small Mersenne Prime Factors (page 741/5610)

Small Mersenne Prime Factors
Prime numbers of the form M_p= 2^p − 1 are called Mersenne primes. For M_p to be prime, p must also be prime.
Any factor q of a Mersenne number 2^p − 1 must be of the form 2kp + 1, where integer k ≥ 0. Furthermore, q must be 1 or 7 mod 8.

Exp.	Prime Factor	Digits	Year
5475293	32851759	8	~1985
5475523	87608369	8	~1986
5475539	10951079	8	~1984
5475557	32853343	8	~1985
5475637	32853823	8	~1985
5475719	10951439	8	~1984
5475721	4588654199	10	~1990
5475881	32855287	8	~1985
5475973	164279191	9	~1987
5475991	54759911	8	~1985
5476283	10952567	8	~1984
5476343	10952687	8	~1984
5476391	43811129	8	~1985
5476511	10953023	8	~1984
5476787	43814297	8	~1985
5476799	131443177	9	~1986
5476813	32860879	8	~1985
5476973	32861839	8	~1985
5477161	32862967	8	~1985
5477399	10954799	8	~1984
5477489	43819913	8	~1985
5477627	43821017	8	~1985
5477779	98600023	8	~1986
5477821	32866927	8	~1985
5478001	32868007	8	~1985

Exp.	Prime Factor	Digits	Year
5478433	32870599	8	~1985
5478569	76699967	8	~1986
5478617	43828937	8	~1985
5478911	10957823	8	~1984
5478937	32873623	8	~1985
5479093	32874559	8	~1985
5479319	10958639	8	~1984
5479403	10958807	8	~1984
5479583	10959167	8	~1984
5479739	10959479	8	~1984
5480081	43840649	8	~1985
5480291	10960583	8	~1984
5480591	10961183	8	~1984
5480723	175383137	9	~1987
5480777	43846217	8	~1985
5480837	43846697	8	~1985
5480879	10961759	8	~1984
5480963	10961927	8	~1984
5481083	10962167	8	~1984
5481097	32886583	8	~1985
5481121	32886727	8	~1985
5481211	54812111	8	~1985
5481251	10962503	8	~1984
5481299	230214559	9	~1987
5481323	10962647	8	~1984

Exp.	Prime Factor	Digits	Year
5481409	383698631	9	~1987
5481431	10962863	8	~1984
5481491	10962983	8	~1984
5481677	43853417	8	~1985
5481811	54818111	8	~1985
5481989	43855913	8	~1985
5482019	10964039	8	~1984
5482097	43856777	8	~1985
5482331	10964663	8	~1984
5482493	32894959	8	~1985
5482781	43862249	8	~1985
5482853	131588473	9	~1986
5482979	10965959	8	~1984
5483227	318027167	9	~1987
5483293	32899759	8	~1985
5483339	10966679	8	~1984
5483399	10966799	8	~1984
5483531	10967063	8	~1984
5483587	54835871	8	~1985
5483671	54836711	8	~1985
5483759	10967519	8	~1984
5483909	43871273	8	~1985
5483977	32903863	8	~1985
5484203	10968407	8	~1984
5484299	10968599	8	~1984

Exp.	Prime Factor	Digits	Year
5484487	54844871	8	~1985
5484887	43879097	8	~1985
5484911	10969823	8	~1984
5484953	131638873	9	~1986
5485163	10970327	8	~1984
5485177	87762833	8	~1986
5485217	76793039	8	~1986
5485603	54856031	8	~1985
5485637	43885097	8	~1985
5485691	10971383	8	~1984
5485691	98742439	8
5485741	32914447	8	~1985
5485757	32914543	8	~1985
5485919	10971839	8	~1984
5486303	10972607	8	~1984
5486339	43890713	8	~1985
5486519	43892153	8	~1985
5486681	43893449	8	~1985
5486879	10973759	8	~1984
5487401	43899209	8	~1985
5487463	186573743	9	~1987
5487791	10975583	8	~1984
5487929	164637871	9	~1987
5487959	10975919	8	~1984
5488031	43904249	8	~1985

5.307.017 digits

26-01-11