A093945 Primes of the form 5*10^n - 1.

499, 4999, 49999, 4999999, 499999999999999, 4999999999999999999999999999999999999999999999999999999

Offset: 1

Author

Rick L. Shepherd, Apr 17 2004

Keywords

• nonn

Comments

Equivalently, primes of the form 4*10^n + 9*R_n, where R_n is the repunit (A002275) of length n.

If m is in the sequence then m appears at the end of m^3, in fact if n>1 and m=5*10^n-1 then m appears at the end of m^3. - Farideh Firoozbakht, Nov 10 2005

If n is in the sequence then 4n is a term of A067206. Namely the digits of 4n end in phi(4n) - the proof is easy. - Farideh Firoozbakht, Dec 30 2006

The next term -- a(7) -- has 211 digits. - Harvey P. Dale, Feb 20 2016

Links

• Makoto Kamada, Prime numbers of the form 499...99.
• Index entries for primes involving repunits.

Crossrefs

Cf. A056712 (corresponding n).

Cf. A067206.

Programs

Mathematica

Select[Table[FromDigits[PadRight[{4},n,9]],{n,60}],PrimeQ] (* Harvey P. Dale, Feb 20 2016 *)