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Super-prime leaders: right-truncatable primes p with property that appending any single decimal digit to p does not produce a prime.
3

%I #21 Feb 16 2025 08:33:21

%S 53,317,599,797,2393,3793,3797,7331,23333,23339,31193,31379,37397,

%T 73331,373393,593993,719333,739397,739399,2399333,7393931,7393933,

%U 23399339,29399999,37337999,59393339,73939133

%N Super-prime leaders: right-truncatable primes p with property that appending any single decimal digit to p does not produce a prime.

%C The name "super-prime leaders" is not due to the author.

%D Joe Roberts, Lure of the Integers, The Mathematical Association of America, 1992, p. 292.

%H Chris Caldwell, The Prime Glossary, <a href="https://t5k.org/glossary/xpage/RightTruncatablePrime.html">Right-truncatable prime</a>

%H G. L. Honaker, Jr. and Chris Caldwell, <a href="https://t5k.org/curios/cpage/10119.html">Prime Curios! 53</a>

%H Kvant magazine, <a href="http://kvant.mccme.ru/1970/11/naiprostejshie_prostye_chisla.htm">The simplest prime numbers</a>, (in Russian) No 11, 1979. (beware of typo)

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TruncatablePrime.html">Truncatable Prime</a>

%H <a href="/index/Tri#tprime">Index entries for sequences related to truncatable primes</a>

%F A024770 INTERSECT A119289.

%e 2393 belongs to this sequence because 2393, 239, 23 and 2 are all prime; 10*2393 + k, for k = 0 to 9, are all composite.

%o (PARI) f=1; for(n=2, 73939133, v=n; t=1; while(isprime(n), if(!Mod(f, n^2)==0, t=t*n); c=n; n=(c-lift(Mod(c, 10)))/10); if(n==0, f=f*t); n=v); s=Set(factor(f)[, 1]); for(k=1, #s, p=s[k]; if(!Mod(f, p^2)==0, print1(p, ", ")));

%Y Subsequence of A024770 and of A119289.

%K nonn,base,fini,full,changed

%O 1,1

%A _Arkadiusz Wesolowski_, Mar 26 2014