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 2021-08-08, 08:48 #254 LaurV Romulan Interpreter     "name field" Jun 2011 Thailand 234238 Posts Aren't mersenne prime palindromes themselves?
2021-08-08, 09:04   #255
paulunderwood

Sep 2002
Database er0rr

109C16 Posts

Quote:
 Originally Posted by LaurV Aren't mersenne prime palindromes themselves?
I base 2 they are. In fact any n>1 is a palindrome in base n+1 and in base n-1

Last fiddled with by paulunderwood on 2021-08-08 at 09:10

2021-08-08, 14:07   #256
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

DEC16 Posts

Quote:
 Originally Posted by LaurV Aren't mersenne prime palindromes themselves?
All primes p not in https://oeis.org/A016038 are palindromes in some base < p-1

 2021-09-11, 08:21 #257 paulunderwood     Sep 2002 Database er0rr 102348 Posts Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1 10^999999 - 1022306*10^287000 - 1 10^999999 - 1087604*10^287000 - 1
2021-09-11, 10:44   #258
Batalov

"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

9,901 Posts

Quote:
 Originally Posted by paulunderwood Congrats to Serge and Ryan for the two smallest known Mega primes, prove with CHG at 28.7% factored of N+1
Two largest known less-than-Mega primes, actually.
(The second one was found before search was called off, an incidental finding. )

Code:
...
10^999999+308267*10^292000+1 	P    1000000  Batalov          02/2021
10^999999+593499	        PRP  1000000  Peter Kaiser     02/2013
10^999999                    	C    1000000  --- a composite, smallest million-digit number
10^999999-172473	        PRP   999999  Patrick De Geest 12/2016
10^999999-1022306*10^287000-1	P     999999  Propper,Batalov  09/2021
10^999999-1087604*10^287000-1	P     999999  Propper,Batalov  09/2021
...

2021-09-11, 16:50   #259
rudy235

Jun 2015
Vallejo, CA/.

21418 Posts

Quote:
 Originally Posted by LaurV Aren't mersenne prime palindromes themselves?
Of course all repunits are “palindromes” per se, but in practical terms when a prime is a Mersenne, a Generalized Mersenne ( to other bases ), repunits, generalized repunits, they are not counted as palindromes in the database of “The primePages”

 2021-09-12, 17:20 #260 paulunderwood     Sep 2002 Database er0rr 10000100111002 Posts Congrats to Marc Wiseler and PrimeGrid for the "321" prime 3*2^17748034-1 (5,342,692 decimal digits) ranked as the 18th largest known prime.
2021-09-12, 17:22   #261
diep

Sep 2006
The Netherlands

31316 Posts

Quote:
 Originally Posted by paulunderwood Congrats to Marc Wiseler and PrimeGrid for the "321" prime 3*2^17748034-1 (5,342,692 decimal digits) ranked as the 18th largest known prime.
Big congrats!!!!!

 2021-09-14, 20:08 #262 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 9,901 Posts Another Riesel "other" number is coming soon. It is a palindrome, chock full of "9"s (with a few others) and is neatly 1,234,567 decimal digits long
2021-09-14, 21:01   #263
paulunderwood

Sep 2002
Database er0rr

22·1,063 Posts

Quote:
 Originally Posted by Batalov Another Riesel "other" number is coming soon. It is a palindrome, chock full of "9"s (with a few others) and is neatly 1,234,567 decimal digits long
I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular reduction.

2021-09-15, 07:15   #264
sweety439

"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36

356410 Posts

Quote:
 Originally Posted by paulunderwood I am looking forward to its revelation. The largest palindrome before this one had 490,001 digits. So 1,234,567 digits is quite amazing considering its crunching is done with generic modular reduction.
https://primes.utm.edu/primes/status.php

id 132704 and 132705 are palindromes.

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