

A187868


Primes of the form 100^k  10^k + 1.


1




OFFSET

1,1


COMMENTS

These primes correspond to k = 2, 4, 6, and 8. There are no other primes of this form for k up to 10000. These primes appear in A187614 because the decimal representation of their reciprocal contains only the digits 0, 1, 8, and 9.
Because these numbers are values of the sixth cyclotomic polynomial, by Theorem 1 of Golomb, the only k that can produce primes are the 3smooth numbers, 2^i*3^j (A003586).


REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 85.


LINKS



MATHEMATICA

Select[Table[100^n  10^n + 1, {n, 1000}], PrimeQ]


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



