Small Mersenne Prime Factors (page 977/5865)

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
8526179	17052359	8	~1985
8526257	460417879	9	~1989
8526359	17052719	8	~1985
8526601	51159607	8	~1986
8526779	358124719	9	~1988
8526941	272862113	9	~1988
8527271	68218169	8	~1987
8527283	17054567	8	~1985
8527331	17054663	8	~1985
8527691	17055383	8	~1985
8527763	17055527	8	~1985
8527781	68222249	8	~1987
8527853	119389943	9	~1987
8528171	17056343	8	~1985
8528183	17056367	8	~1985
8528357	68226857	8	~1987
8528519	17057039	8	~1985
8528783	17057567	8	~1985
8528867	68230937	8	~1987
8529197	51175183	8	~1986
8529299	153527383	9	~1987
8529611	17059223	8	~1985
8529623	17059247	8	~1985
8529623	426481151	9
8529863	17059727	8	~1985

Exp.	Prime Factor	Digits	Year
8530037	68240297	8	~1987
8530219	8120768489	10	~1992
8530241	409451569	9	~1989
8530273	51181639	8	~1986
8530307	68242457	8	~1987
8530441	51182647	8	~1986
8530799	68246393	8	~1987
8530811	17061623	8	~1985
8531221	51187327	8	~1986
8531233	51187399	8	~1986
8531473	801958463	9	~1989
8531483	17062967	8	~1985
8531533	51189199	8	~1986
8531609	255948271	9	~1988
8531639	17063279	8	~1985
8531849	68254793	8	~1987
8531879	17063759	8	~1985
8531881	136510097	9	~1987
8532221	51193327	8	~1986
8532269	324226223	9	~1988
8532371	17064743	8	~1985
8532421	187713263	9	~1988
8532541	51195247	8	~1986
8532659	17065319	8	~1985
8532899	68263193	8	~1987

Exp.	Prime Factor	Digits	Year
8533139	17066279	8	~1985
8533537	51201223	8	~1986
8533559	17067119	8	~1985
8533619	68268953	8	~1987
8533697	51202183	8	~1986
8533799	68270393	8	~1987
8533979	17067959	8	~1985
8534041	51204247	8	~1986
8534069	68272553	8	~1987
8534243	17068487	8	~1985
8534303	17068607	8	~1985
8534371	85343711	8	~1987
8534411	17068823	8	~1985
8534411	153619399	9
8534423	17068847	8	~1985
8534447	68275577	8	~1987
8534639	17069279	8	~1985
8534657	68277257	8	~1987
8534891	17069783	8	~1985
8535083	17070167	8	~1985
8535179	17070359	8	~1985
8535413	51212479	8	~1986
8535433	51212599	8	~1986
8535473	51212839	8	~1986
8535533	51213199	8	~1986

Exp.	Prime Factor	Digits	Year
8535781	51214687	8	~1986
8535847	136573553	9	~1987
8535929	68287433	8	~1987
8536043	17072087	8	~1985
8536267	85362671	8	~1987
8536571	17073143	8	~1985
8536807	85368071	8	~1987
8536883	17073767	8	~1985
8537219	17074439	8	~1985
8537437	51224623	8	~1986
8537467	85374671	8	~1987
8537603	17075207	8	~1985
8537747	68301977	8	~1987
8538143	17076287	8	~1985
8538371	17076743	8	~1985
8538599	631856327	9	~1989
8538611	17077223	8	~1985
8538833	51232999	8	~1986
8538851	17077703	8	~1985
8539051	85390511	8	~1987
8539057	51234343	8	~1986
8539067	204937609	9	~1988
8539259	17078519	8	~1985
8539259	68314073	8
8539691	17079383	8	~1985

5.561.074 digits

26-05-10