20211130, 06:07  #1 
"Καλός"
May 2018
2^{6}·5 Posts 
Palindromic Prime Exponents
Out of the total of 5,953 base10 palindromic prime exponents < 10^{9}, currently there are 1,889 remaining base10 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 base10 palindromic prime exponents.

20211130, 14:40  #2 
"Καλός"
May 2018
500_{8} Posts 
The initial post contains a list of base10 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 CLL/CPRP status (see the attached file). 
20220306, 21:20  #3 
"Καλός"
May 2018
2^{6}·5 Posts 
The following Wolfram language code generates the remaining palindromic prime exponents < 10^{9} 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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