20211128, 17:20  #221 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5×7×89 Posts 
These are all minimal primes (start with b+1) in base b=25 up to 2^32
Base 25 is a very hard base (however, of course, bases > 25 which are coprime to 6 are harder than it), we can imagine an alien force, vastly more powerful than us, landing on Earth and demanding the set of minimal primes (start with b+1) in base b=17 (or 19, 21, 22, 23, 28, 30, 36) (including primality proving of the probable primes in this set) or they will destroy our planet. In that case, I claim, we should marshal all our computers and all our mathematicians and attempt to find the set and to prove the primality of all numbers in this set. But suppose, instead, that they ask for the set of minimal primes (start with b+1) in base b=25 (or 26, 27, 29, 31, 32, 33, 34, 35). In that case, I believe, we should attempt to destroy the aliens. Last fiddled with by sweety439 on 20211128 at 18:46 
20211128, 17:23  #222  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5·7·89 Posts 
Quote:
very important note: they are minimal primes (start with b'+1) in base b'=b^2 instead of base b'=b Last fiddled with by sweety439 on 20211128 at 17:25 

20211130, 19:59  #223 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
110000101011_{2} Posts 
more datas

20211130, 20:41  #224  
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5·7·89 Posts 
Quote:
The string is of the form {0}S{0,2,4,5,6,8} and S is of one of these forms: * empty string * "gcd of its digits" <> 1 (note: gcd(0,n) = n for all n, including n=0) * X{0}Y with X+Y divisible by 3 (this includes: 2{0}1, 2{0}7, 5{0}1, 5{0}7, 8{0}1, 8{0}7) * 28{0}7 * 4{6}9 * 221 * 2021 * 2201 * 22001 * 220001 * 2200001 * (5^n)1 with n<11 * 581 * 5(0^n)27 with n<28 * 5207 * 52007 * 520007 * 649 * 6649 * 66649 * 6049 * 60049 * 600049 * 6000049 * 66049 * 660049 * 6600049 * 666049 * 6660049 * 8(5^n)1 with n<11 * 8051 * 80551 * 805551 * 8055551 * 91 * 901 * 921 * 951 * 981 * 9021 * 9051 * 9081 * 9201 * 9501 * 9581 * 9801 * 90581 * 95081 * 949 * 9469 * 94669 reference: https://math.stackexchange.com/quest...enumberinit Last fiddled with by sweety439 on 20211130 at 20:47 

20211130, 20:52  #225 
"99(4^34019)99 palind"
Nov 2016
(P^81993)SZ base 36
5·7·89 Posts 
Update data for minimal primes, see https://sites.google.com/view/dataofminimalprimes

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