20220204, 23:12  #12 
"Rashid Naimi"
Oct 2015
Remote to Here/There
2^{4}×11×13 Posts 
https://www.wolframalpha.com/input?i..._12+to+base+10
https://www.wolframalpha.com/input?i=168526123+is+prime https://www.mersenne.org/report_expo...526123&exp_hi= Last fiddled with by a1call on 20220204 at 23:14 
20220204, 23:19  #13 
Sep 2002
Database er0rr
3^{4}·53 Posts 
I see. Convert to base 10 from base 12. Silly me. Got for it Tucker! No one is stopping you. Good luck!
(I initially thought that T. was saying that converting a prime to another base somehow changed its primeness. Sorry). Last fiddled with by paulunderwood on 20220204 at 23:23 
20220205, 00:16  #14  
"Καλός"
May 2018
16D_{16} Posts 
Quote:


20220205, 00:53  #15  
"Καλός"
May 2018
5·73 Posts 
Quote:
Offtopic: Throughout the Chinese Lunar Year Huangdi (Yellow Emperor) 4720 (2022) of the Water Tiger, lucky numbers allegedly are 1, 3, and 4 as well as numerals that contain them such as 14 and 34. The digit sum of 168,526,123 is 34 and there is no known Mersenne prime having an exponent with said digit sum. :) 

20220208, 05:17  #16 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}·73 Posts 
Other than singledigit primes (2, 3, 5, 7), can a Mersenne exponent be a palindromic prime?

20220208, 19:09  #17  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
2·3·5·229 Posts 
Quote:
So we already know there are no (base 10) palindromic exponent Mersenne primes between exponents: 11.  60M & probably to 107M; 200M300M; 400M700M; 800M900M; leaving 60M likely 107M  200M, 300M  400M, 700M  800M, 900M+. The odds get worse for 10 or more digit exponents. https://www.mersenneforum.org/showpo...46&postcount=5 Changing bases, there are more. Consider base two. 3, 5, 7, 17, 31, 107, 127. Last fiddled with by kriesel on 20220208 at 19:10 

20220208, 19:14  #18 
If I May
"Chris Halsall"
Sep 2002
Barbados
2×19×281 Posts 
I know it's not easy to do...
But... I keep being told by those I trust that speaking into a vacuum means (by definition) that few actually receive your message. Some may see your lips move (read: see your language), but few can lipread (read: read and parce). 
20220208, 20:36  #19  
Feb 2017
Nowhere
3·1,999 Posts 
Quote:
For positive integer k, the number of 2*k + 1 digit palindromic numbers to base ten is 9*10^{k} (9 possible nonzero digits for the first and last digit, ten possible middle digits, and an arbitrary block of k1 digits in between). Of these, 4*10^{k} are relatively prime to 10. Apart from that, I have no idea of the likelihood of a palindromic number of 2*k + 1 decimal digits being prime. Under the "assumption of ignorance" that the likelihood is the same as a random odd number prime to 10, something on the order of 1/(2*k*log(10)) of them would be prime. But the total number of palindromic numbers is tiny compared to the number of primes if k is large. The number of primes with 2*k + 1 decimal digits is roughly 9*10^{2k}/((2k)*log(10)), so the odds of a 2k+ 1 digit prime being palindromic are less than 8*k*log(10)/9 in 10^{k}. Under the "assumption of ignorance" the odds would be something like 4/9 in 10^{k} (unless I botched the calculation, of course) 

20220321, 18:39  #20 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
R49081 is now proven prime, see post https://mersenneforum.org/showpost.p...9&postcount=35

20220322, 11:33  #21  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
7^{2}×73 Posts 
Quote:
Pocklington N1 primality test > Proth primality test > Pépin primality test for Fermat numbers Morrison N+1 primality test > Lucas–Lehmer–Riesel primality test > Lucas–Lehmer primality test for Mersenne numbers However, for R49081, neither N1 nor N+1 can be trivially >= 33.3333% factored, thus ECPP primality test (such PRIMO) is needed to use, thus they are very different. See top definitely primes and top probable primes, for the top definitely primes, (usually) one of N1 and N+1 is trivially 100% factored, while for top probable primes, none of them can be >= 33.3333% factored. Last fiddled with by sweety439 on 20220322 at 11:35 

20220322, 15:05  #22  
Jun 2015
Vallejo, CA/.
3×13×29 Posts 
Quote:
See https://www.ams.org/journals/mcom/19...08567143.pdf 

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