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A186995 Smallest weak prime in base n. 5
127, 2, 373, 83, 28151, 223, 6211, 2789, 294001, 3347, 20837899, 4751, 6588721, 484439, 862789, 10513, 2078920243, 10909, 169402249, 2823167, 267895961, 68543, 1016960933671, 181141, 121660507, 6139219, 11646280537, 488651 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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.

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

a(24) > 10^11. - Jon E. Schoenfield, May 06 2019

a(30) > 2*10^12. - Giovanni Resta, Jun 17 2019

LINKS

Table of n, a(n) for n=2..29.

Terence Tao, A remark on primality testing and decimal expansions, arXiv:0802.3361 [math.NT], 2008.

Terence Tao, A remark on primality testing and decimal expansions, Journal of the Australian Mathematical Society 91:3 (2011), pp. 405-413.

Eric W. Weisstein, MathWorld: Weakly Prime

MATHEMATICA

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}]

CROSSREFS

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

Sequence in context: A212927 A300785 A051335 * A145586 A180352 A217557

Adjacent sequences:  A186992 A186993 A186994 * A186996 A186997 A186998

KEYWORD

nonn,base,more

AUTHOR

T. D. Noe, Mar 01 2011

EXTENSIONS

a(17)-a(23) from Terentyev Oleg, Sep 04 2011

a(24)-a(29) from Giovanni Resta, Jun 17 2019

STATUS

approved

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Last modified November 22 02:58 EST 2019. Contains 329383 sequences. (Running on oeis4.)