A020994 Primes that are both left-truncatable and right-truncatable.

2, 3, 5, 7, 23, 37, 53, 73, 313, 317, 373, 797, 3137, 3797, 739397

Offset: 1

Author

Mario Velucchi (mathchess(AT)velucchi.it)

Keywords

• nonn
• fini
• full
• base

Comments

Two-sided primes: deleting any number of digits at left or at right, but not both, leaves a prime.

Primes in which every digit string containing the most significant digit or the least significant digit is prime. - Amarnath Murthy, Sep 24 2003

Intersection of A024785 and A024770. - Robert Israel, Mar 23 2015

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers, p. 178 (Rev. ed. 1997).

Links

• I. O. Angell and H. J. Godwin, On Truncatable Primes Math. Comput. 31, 265-267, 1977.
• Patrick De Geest, The list of 4260 left-truncatable primes
• Index entries for sequences related to truncatable primes

Crossrefs

Cf. A033664, A024785, A032437, A024770, A052023, A052024, A052025, A050986, A050987, A254751, A254753.

Programs

Mathematica

tspQ[n_] := Module[{idn=IntegerDigits[n], l}, l=Length[idn]; Union[PrimeQ/@(FromDigits/@ Join[Table[Take[idn, i], {i, l}], Table[Take[idn, -i], {i, l}]])]=={True}] Select[Prime[Range[PrimePi[740000]]], tspQ]

Extensions

Corrected by David W. Wilson

Additional comments from Harvey P. Dale, Jul 10 2002