mersenneforum.org Palindromic Prime Exponents
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2021-11-30, 06:07   #1
Dobri

"Καλός"
May 2018

1010000112 Posts
Palindromic Prime Exponents

Out of the total of 5,953 base-10 palindromic prime exponents < 109, currently there are 1,889 remaining base-10 palindromic prime exponents for which the corresponding Mersenne numbers have no known factor (see the attached file). The list does not include the exponents for M2, M3, M5, and M7 which are the only four known Mersenne primes with base-10 palindromic prime exponents.
Attached Files
 PalindromicExponents_UnfactoredMersenneNumbers.txt (40.6 KB, 62 views)

2021-11-30, 14:40   #2
Dobri

"Καλός"
May 2018

17·19 Posts

The initial post contains a list of base-10 palindromic prime exponents for which currently the corresponding Mersenne numbers have no known factor and are also of untested or unverified LL/PRP status.
In addition, this second post contains a shorter list of 292 exponents for which currently the corresponding Mersenne numbers have no known factor but are of verified C-LL/C-PRP status (see the attached file).
Attached Files
 PalindromicExponents_VerifiedMersenneNumbers.txt (2.7 KB, 64 views)

 2022-03-06, 21:20 #3 Dobri   "Καλός" May 2018 1010000112 Posts The following Wolfram language code generates the remaining palindromic prime exponents < 109 for which the corresponding Mersenne numbers remain to be factored/verified. Currently, there are 1880 such palindromic exponents within the range [100707001,..., 999676999]. Note that the code could be optimized for speed. Code: pp = PrimePi[10^9]; pn = 1; count = 0; ic = 1; While[ic <= pp, pn = NextPrime[pn]; If[(PalindromeQ[pn] == True) && (pn > 7), pns = ToString[pn]; wppns = StringJoin["https://www.mersenne.org/report_exponent/?exp_lo=", pns, "&exp_hi=&text=1"]; text = Import[wppns]; fc = StringContainsQ[text, "Factored"]; vc = StringContainsQ[text, "Verified"]; If[(fc == False) && (vc == False), Print[pn]; count++;]; ]; ic++;]; Print[count];

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