This site is supported by donations to The OEIS Foundation.



Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A186995 Smallest weak prime in base n. 5


%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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