A143641 Odd prime-proof numbers (A118118) not ending in 5.

212159, 595631, 872897, 1203623, 1293671, 1566691, 1702357, 1830661, 3716213, 3964169, 4103917, 4134953, 4173921, 4310617, 4376703, 4586509, 4703801, 4749187, 4801387, 4928909, 5005353, 5051179, 5231739, 5258901, 5317573

Offset: 1

Author

M. F. Hasler, Aug 27 2008, Sep 04 2008

Keywords

• base
• nonn

Comments

Most "prime-proof" numbers are even or multiples of 5, cf. A118118.

Nicol & Selfridge proved that this sequence is infinite. - Charles R Greathouse IV, Jan 27 2014

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..3655 from Klaus Brockhaus)
• Michael Filaseta, Mark Kozek, Charles Nicol and John Selfridge, Composites that remain composite after changing a digit, Journal of Combinatorics and Number Theory 2 (2011), pp. 25-36.
• Project Euler, Problem 200: Prime-proof Squbes (2008).

Crossrefs

Cf. A118118.

Programs

Magma

IsA143641:=function(n); D:=Intseq(n); return Intseq(n)[1] ne 5 and forall{ : k in [1..#D], j in [0..9] | not IsPrime(Seqint(Insert(D, k, k, [j]))) }; end function; [ n: n in [1..4000000 by 2] | IsA143641(n) ]; // Klaus Brockhaus, Mar 03 2011

PARI

forstep( i=1,10^7,2, i%5 || next; isA118118(i) && print1(i","))

Python

from sympy import isprime
from itertools import count, islice
def selfplusneighs(n):
    s = str(n); d = "0123456789"; L = len(s)
    yield from (int(s[:i]+c+s[i+1:]) for c in d for i in range(L))
def agen():
    for n in count(1, 2):
        if n%5 == 0: continue
        if all(not isprime(k) for k in selfplusneighs(n)):
            yield n
print(list(islice(agen(), 8))) # Michael S. Branicky, Aug 16 2022