Small Mersenne Prime Factors (page 997/5670)

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
8996831	17993663	8	~1985
8997011	17994023	8	~1985
8997239	17994479	8	~1985
8997311	17994623	8	~1985
8997503	17995007	8	~1985
8997553	143960849	9	~1988
8997869	125970167	9	~1987
8997871	89978711	8	~1987
8998271	17996543	8	~1985
8998307	71986457	8	~1987
8998651	161975719	9	~1988
8998883	17997767	8	~1985
8998919	17997839	8	~1985
8999051	17998103	8	~1985
8999183	17998367	8	~1985
8999423	17998847	8	~1985
8999777	71998217	8	~1987
9000203	18000407	8	~1985
9000577	54003463	8	~1986
9000637	54003823	8	~1986
9000683	18001367	8	~1985
9000709	198015599	9	~1988
9000721	144011537	9	~1988
9001163	810104671	9	~1989
9001337	54008023	8	~1986

Exp.	Prime Factor	Digits	Year
9001387	576088769	9	~1989
9001511	18003023	8	~1985
9001799	18003599	8	~1985
9001933	54011599	8	~1986
9002249	72017993	8	~1987
9002621	270078631	9	~1988
9002849	72022793	8	~1987
9003583	90035831	8	~1987
9004091	72032729	8	~1987
9004343	18008687	8	~1985
9004469	72035753	8	~1987
9004561	54027367	8	~1986
9004571	18009143	8	~1985
9004643	18009287	8	~1985
9004739	18009479	8	~1985
9004739	72037913	8
9005039	18010079	8	~1985
9005041	54030247	8	~1986
9005099	18010199	8	~1985
9005201	54031207	8	~1986
9005327	162095887	9	~1988
9005519	18011039	8	~1985
9005741	54034447	8	~1986
9005879	72047033	8	~1987
9006071	18012143	8	~1985

Exp.	Prime Factor	Digits	Year
9006359	18012719	8	~1985
9006509	72052073	8	~1987
9006649	216159577	9	~1988
9006677	72053417	8	~1987
9006919	216166057	9	~1988
9006973	54041839	8	~1986
9007151	18014303	8	~1985
9007241	72057929	8	~1987
9007457	54044743	8	~1986
9007457	72059657	8
9007657	486413479	9	~1989
9007703	18015407	8	~1985
9007811	18015623	8	~1985
9008141	54048847	8	~1986
9008771	18017543	8	~1985
9008809	216211417	9	~1988
9008873	54053239	8	~1986
9009023	18018047	8	~1985
9009191	18018383	8	~1985
9009419	18018839	8	~1985
9009551	18019103	8	~1985
9009551	72076409	8
9010007	504560393	9	~1989
9010433	54062599	8	~1986
9010633	54063799	8	~1986

Exp.	Prime Factor	Digits	Year
9010751	18021503	8	~1985
9010853	54065119	8	~1986
9010979	18021959	8	~1985
9010979	72087833	8
9011279	72090233	8	~1987
9011459	72091673	8	~1987
9011771	18023543	8	~1985
9012097	54072583	8	~1986
9012131	18024263	8	~1985
9012299	18024599	8	~1985
9012383	18024767	8	~1985
9012611	18025223	8	~1985
9012911	18025823	8	~1985
9012911	72103289	8
9013019	18026039	8	~1985
9013061	72104489	8	~1987
9013271	18026543	8	~1985
9013271	72106169	8
9013463	18026927	8	~1985
9013561	54081367	8	~1986
9013853	54083119	8	~1986
9013853	126193943	9
9014023	90140231	8	~1987
9014023	378588967	9
9014039	18028079	8	~1985

5.366.787 digits

26-02-08