Perry numbers - formerly known as "Wilde Primes"
- Hey guys! I've recently done some more work on so-called "Wilde
Primes" although I suggest that if we keep any of Jon Perry's name we
should call them "Perry numbers" by analogy with Riesel and
Under my proposed naming scheme, a Perry number k is never prime no
matter how many 1s you add to the right hand side of its base-10
representation. Primes thus obtained would be Perry primes. Although
the default base would be 10, Perry numbers and Perry primes exist in
other bases although perhaps the non base-10 cases could be subsumed
under a generalization of Riesel and Sierpinski numbers. We could
therefore alternatively describe Perry numbers as base-10 Riesel
We are therefore looking for numbers k for which ((9k+1)*10^n-1)/9 is
never prime. Jack Brennen conjectured that 176 is the lowest Perry as
it has a covering set using the primes 3, 7, 11 and 13. Four lower
candidates existed but eventually fairly large Perry probable primes
were found for three of these values. One of these probable primes
was confirmed as prime using Primo. Another should be provable using
current methods but the third will be impossible using general
primality proving software. Perhaps Proth's theorem can be extended
to bases other than 2? ;-)
I am pleased to announce, however, that Jack Brennen's conjecture is
false as I have proved that 38 is the smallest Perry number. It's
quite interesting to see why. I commend this problem to you as one
where the aesthetics of the result are disproportionately high given
the ease of the solution.
> I am pleased to announce, however, that Jack Brennen's conjecture isClear as day, now that it's been pointed out.
> false as I have proved that 38 is the smallest Perry number.
After all, who could possibly miss the fact that 38 equals (7^3-1)/9...