A239747 Super-prime leaders: right-truncatable primes p with property that appending any single decimal digit to p does not produce a prime.

53, 317, 599, 797, 2393, 3793, 3797, 7331, 23333, 23339, 31193, 31379, 37397, 73331, 373393, 593993, 719333, 739397, 739399, 2399333, 7393931, 7393933, 23399339, 29399999, 37337999, 59393339, 73939133

Offset: 1

Author

Arkadiusz Wesolowski, Mar 26 2014

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

			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.
		

References

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

Links

• Chris Caldwell, The Prime Glossary, Right-truncatable prime
• G. L. Honaker, Jr. and Chris Caldwell, Prime Curios! 53
• Kvant magazine, The simplest prime numbers, (in Russian) No 11, 1979. (beware of typo)
• Eric Weisstein's World of Mathematics, Truncatable Prime
• Index entries for sequences related to truncatable primes

Crossrefs

Subsequence of A024770 and of A119289.

Programs

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, ", ")));

Formula

A024770 INTERSECT A119289.