Small Mersenne Prime Factors (page 1033/6045)

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
9219923	18439847	8	~1985
9220019	18440039	8	~1985
9220163	18440327	8	~1985
9220181	55321087	8	~1987
9220331	18440663	8	~1985
9220459	92204591	8	~1987
9220559	18441119	8	~1985
9220583	18441167	8	~1985
9220621	55323727	8	~1987
9220721	55324327	8	~1987
9221657	55329943	8	~1987
9221711	18443423	8	~1985
9221747	73773977	8	~1987
9221753	55330519	8	~1987
9221867	73774937	8	~1987
9221879	73775033	8	~1987
9221921	55331527	8	~1987
9221921	73775369	8
9222179	18444359	8	~1985
9222443	18444887	8	~1985
9222589	221342137	9	~1988
9222659	18445319	8	~1985
9222671	73781369	8	~1987
9223321	55339927	8	~1987
9223387	92233871	8	~1987

Exp.	Prime Factor	Digits	Year
9223573	55341439	8	~1987
9223597	147577553	9	~1988
9223649	73789193	8	~1987
9223751	18447503	8	~1985
9224323	92243231	8	~1987
9224399	18448799	8	~1985
9224837	129147719	9	~1987
9224927	73799417	8	~1987
9224983	221399593	9	~1988
9225179	18450359	8	~1985
9225221	55351327	8	~1987
9225539	18451079	8	~1985
9225719	18451439	8	~1985
9225947	166067047	9	~1988
9226391	18452783	8	~1985
9226439	18452879	8	~1985
9226753	221442073	9	~1988
9227041	147632657	9	~1988
9227221	719723239	9	~1989
9227297	73818377	8	~1987
9227321	55363927	8	~1987
9227357	55364143	8	~1987
9227579	18455159	8	~1985
9227579	73820633	8
9227627	73821017	8	~1987

Exp.	Prime Factor	Digits	Year
9227741	885863137	9	~1990
9227849	295291169	9	~1988
9227879	73823033	8	~1987
9228203	221476873	9	~1988
9228311	18456623	8	~1985
9228419	73827353	8	~1987
9228599	18457199	8	~1985
9228689	129201647	9	~1987
9229439	18458879	8	~1985
9229523	18459047	8	~1985
9229673	55378039	8	~1987
9229699	92296991	8	~1987
9229721	73837769	8	~1987
9230183	18460367	8	~1985
9230317	276909511	9	~1988
9230357	55382143	8	~1987
9230369	73842953	8	~1987
9230437	55382623	8	~1987
9230579	73844633	8	~1987
9230737	55384423	8	~1987
9230911	92309111	8	~1987
9230999	18461999	8	~1985
9232259	18464519	8	~1985
9232631	18465263	8	~1985
9232711	535497239	9	~1989

Exp.	Prime Factor	Digits	Year
9232957	221590969	9	~1988
9233123	738649841	9	~1989
9233201	73865609	8	~1987
9233219	18466439	8	~1985
9233579	18467159	8	~1985
9233659	221607817	9	~1988
9233743	92337431	8	~1987
9233821	55402927	8	~1987
9233837	73870697	8	~1987
9234299	18468599	8	~1985
9234359	18468719	8	~1985
9234479	18468959	8	~1985
9234479	387848119	9
9234517	55407103	8	~1987
9234713	55408279	8	~1987
9235511	18471023	8	~1985
9235559	18471119	8	~1985
9235703	18471407	8	~1985
9235739	166243303	9	~1988
9235823	18471647	8	~1985
9235847	609565903	9	~1989
9235931	18471863	8	~1985
9236327	73890617	8	~1987
9236657	73893257	8	~1987
9236663	18473327	8	~1985

5.740.663 digits

26-08-02