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A186995 Smallest weak prime in base n. 5

%I

%S 127,2,373,83,28151,223,6211,2789,294001,3347,20837899,4751,6588721,

%T 484439,862789,10513,2078920243,10909,169402249,2823167,267895961,

%U 68543,1016960933671,181141,121660507,6139219,11646280537,488651

%N Smallest weak prime in base n.

%C In base b, a prime is said to be weakly prime if changing any digit produces only composite numbers. Tao proves that in any fixed base there are an infinite number of weakly primes.

%C In particular, changing the leading digit to 0 must produce a composite number. These are also called weak primes, weakly primes, and isolated primes. - _N. J. A. Sloane_, May 06 2019

%C a(24) > 10^11. - _Jon E. Schoenfield_, May 06 2019

%C a(30) > 2*10^12. - _Giovanni Resta_, Jun 17 2019

%H Terence Tao, <a href="https://arxiv.org/abs/0802.3361">A remark on primality testing and decimal expansions</a>, arXiv:0802.3361 [math.NT], 2008.

%H Terence Tao, <a href="https://doi.org/10.1017/S1446788712000043">A remark on primality testing and decimal expansions</a>, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405-413.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/WeaklyPrime.html">MathWorld: Weakly Prime</a>

%t isWeak[n_, base_] := Module[{d, e, weak, num}, d = IntegerDigits[n, base]; weak = True; Do[e = d; e[[i]] = j; num = FromDigits[e, base]; If[num != n && PrimeQ[num], weak = False; Break[]], {i, Length[d]}, {j, 0, base - 1}]; weak]; Table[p = 2; While[! isWeak[p, n], p = NextPrime[p]]; p, {n, 2, 16}]

%Y Cf. A050249 (base 10), A137985 (base 2).

%K nonn,base,more

%O 2,1

%A _T. D. Noe_, Mar 01 2011

%E a(17)-a(23) from _Terentyev Oleg_, Sep 04 2011

%E a(24)-a(29) from _Giovanni Resta_, Jun 17 2019

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)