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Old 2021-11-30, 06:07   #1
Dobri
 
"刀-比-日"
May 2018

317 Posts
Default 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.
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File Type: txt PalindromicExponents_UnfactoredMersenneNumbers.txt (40.6 KB, 53 views)
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Old 2021-11-30, 14:40   #2
Dobri
 
"刀-比-日"
May 2018

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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).
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File Type: txt PalindromicExponents_VerifiedMersenneNumbers.txt (2.7 KB, 56 views)
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Old 2022-03-06, 21:20   #3
Dobri
 
"刀-比-日"
May 2018

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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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