Small Mersenne Prime Factors (page 349/5340)

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
1696069	37313519	8	~1982
1696157	23746199	8	~1982
1696199	54278369	8	~1983
1696207	152658631	9	~1984
1696501	37323023	8	~1982
1696511	3393023	7	~1980
1696517	135721361	9	~1984
1696571	13572569	8	~1981
1696579	57683687	8	~1983
1696601	13572809	8	~1981
1696811	3393623	7	~1980
1696861	10181167	8	~1981
1696951	27151217	8	~1982
1696979	3393959	7	~1980
1697243	3394487	7	~1980
1697287	27156593	8	~1982
1697309	13578473	8	~1981
1697309	64497743	8
1697357	13578857	8	~1981
1697419	108634817	9	~1983
1697461	10184767	8	~1981
1697519	3395039	7	~1980
1697533	241049687	9	~1984
1697623	27161969	8	~1982
1697767	27164273	8	~1982

Exp.	Prime Factor	Digits	Year
1698023	3396047	7	~1980
1698077	13584617	8	~1981
1698247	27171953	8	~1982
1698289	37362359	8	~1982
1698569	23779967	8	~1982
1698679	40768297	8	~1982
1698797	10192783	8	~1981
1698857	10193143	8	~1981
1698857	23783999	8
1698869	54363809	8	~1983
1699153	37381367	8	~1982
1699157	91754479	8	~1983
1699213	67968521	8	~1983
1699319	3398639	7	~1980
1699333	118953311	9	~1983
1699391	13595129	8	~1981
1699597	27193553	8	~1982
1699619	40790857	8	~1982
1699667	30594007	8	~1982
1699679	3399359	7	~1980
1699783	67991321	8	~1983
1699787	13598297	8	~1981
1699799	13598393	8	~1981
1700107	612038521	9	~1985
1700219	30603943	8	~1982

Exp.	Prime Factor	Digits	Year
1700233	78210719	8	~1983
1700267	95214953	8	~1983
1700339	13602713	8	~1981
1700353	27205649	8	~1982
1700423	3400847	7	~1980
1700591	3401183	7	~1980
1700617	68024681	8	~1983
1700683	27210929	8	~1982
1700819	30614743	8	~1982
1700987	30617767	8	~1982
1701059	54433889	8	~1983
1701061	10206367	8	~1981
1701137	13609097	8	~1981
1701137	51034111	8
1701179	3402359	7	~1980
1701263	3402527	7	~1980
1701437	13611497	8	~1981
1701461	54446753	8	~1983
1701493	37432847	8	~1982
1701523	68060921	8	~1983
1701571	17015711	8	~1981
1701643	27226289	8	~1982
1701643	40839433	8
1701643	68065721	8
1701731	626237009	9	~1985

Exp.	Prime Factor	Digits	Year
1701743	3403487	7	~1980
1701851	3403703	7	~1980
1701857	10211143	8	~1981
1702061	51061831	8	~1983
1702139	3404279	7	~1980
1702237	51067111	8	~1983
1702319	40855657	8	~1982
1702417	40858009	8	~1982
1702511	3405023	7	~1980
1702627	17026271	8	~1981
1702639	17026391	8	~1981
1702663	17026631	8	~1981
1702663	326911297	9
1702741	10216447	8	~1981
1702901	10217407	8	~1981
1702963	57900743	8	~1983
1703159	40875817	8	~1982
1703231	3406463	7	~1980
1703231	13625849	8
1703231	112413247	9
1703269	37471919	8	~1982
1703323	17033231	8	~1981
1703381	13627049	8	~1981
1703399	13627193	8	~1981
1703599	30664783	8	~1982

5.037.460 digits

25-09-07