A255669 Primes p such that p divides the concatenation of the next two primes.

3, 7, 61, 167

Offset: 1

Author

Harvey P. Dale, Mar 01 2015

Keywords

• nonn
• base

Comments

No additional terms up to the 5-millionth prime. Is the sequence finite and complete?

No additional terms up to the billionth prime. - Chai Wah Wu, Mar 10 2015

a(5) > 10^18. If the reasonable assumption nextprime(p) < p + (log p)^2 holds, then a(5) > 10^53. However, the 192-digits prime

7046979865771812080536912751677852348993288590604026845637583892...

6174496644295302013422818791946308724832214765100671140939597315...

4362416107382550335570469798657718120805369127516778523489932887 is in the sequence. - Giovanni Resta, May 08 2015

Examples

			The three primes beginning with 61 are 61, 67, and 71, and 61 evenly divides 6771.
		

Programs

Mathematica

divQ[{a_,b_,c_}]:=Divisible[FromDigits[Flatten[IntegerDigits/@{b,c}]],a]; Transpose[Select[Partition[Prime[Range[500]],3,1],divQ]][[1]]

Python

from sympy import nextprime
A255669_list, p1, p2, l = [], 2, 3, 10
for n in range(10**8):
    p3 = nextprime(p2)
    if p3 >= l: # this test is sufficient by Bertrand-Chebyshev theorem
        l *= 10
    if not ((p2 % p1)*l + p3) % p1:
        A255669_list.append(p1)
    p1, p2 = p2, p3 # Chai Wah Wu, Mar 09 2015