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Old 2019-05-22, 20:00   #3
kriesel
 
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Default Statistics of Mersenne number factors found

A table of numbers of exponents with 0 to 7 factors under 2^65 is available at https://www.mersenneforum.org/showpo...1&postcount=46

Fully factored exponents show higher prevalence of p=3 mod 4 than p=1 mod 4. https://www.mersenneforum.org/showpo...4&postcount=62 And the ratio rises as they are screened for p > increasing thresholds.

Semiprime exponents show higher prevalence of p=3 mod 4 than p=1 mod 4. https://www.mersenneforum.org/showpo...5&postcount=69
And the ratio rises to 2:1 as they are screened for p > increasing thresholds.

Exponents p = 3 mod 4 have slightly more factors found, than p= 1 mod 4. https://www.mersenneforum.org/showpo...4&postcount=77

Also f=1 mod 8 has fewer factors found than f=7 mod 8, by about 12%. https://www.mersenneforum.org/showpo...6&postcount=80

Combining consideration of f = 1 or 7 mod 8 and 1 or 5 mod 6, f = 1, 7, 17, or 23 mod 24.
"for exponents p=3 (mod 4), factors that are f=23 (mod 24) are found about one-third more frequently than the other kinds."
https://www.mersenneforum.org/showpo...7&postcount=85

Known factors and other info can be downloaded from links at https://www.mersenneforum.org/showpo...1&postcount=11 for p<109; for above, at https://www.mersenneforum.org/showpo...54&postcount=9

Wagstaff paper: Divisors of Mersenne Numbers, MATHEMATICS OF COMPUTATION VOLUME 40, NUMBER 161 JANUARY 1983. PAGES 385-397
http://www.ams.org/journals/mcom/198...-0679454-X.pdf


Top of reference tree: https://www.mersenneforum.org/showpo...22&postcount=1

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