A046284 Primes p such that concatenation of primes from 2 through p is a prime.

2, 3, 7, 719, 1033, 2297, 3037, 11927

Offset: 1

Author

Patrick De Geest, Jun 15 1998

Keywords

• nonn
• base

Comments

"w_n = (P_1)(P_2) ... (P_n) [A019518], by which notation we mean that w_n is constructed in decimal by simple concatenation of digits [much like the Almost Natural numbers (A007376)]. For example, the first few w_n are 2, 23, 235, 2357, 235711, ... ." - Crandall and Pomerance

Examples

			7 is a member, since 2357 is a prime.
		

References

• R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that 5441 is a term.]

Links

• Eric Weisstein's World of Mathematics, Consecutive Number Sequences.
• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Smarandache-Wellin Number

Crossrefs

Cf. A019518, A033308, A069151. a(n) = prime(A046035(n)).

Programs

Mathematica

a = ""; Do[a = StringJoin[a, ToString[ Prime[n]]]; If[ PrimeQ[ ToExpression[a]], Print[n]], {n, 1, 1429}]

Extensions

Additional comments from Robert G. Wilson v, Sep 10 2001