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

Sierpinski numbers.

http://www.users.globalnet.co.uk/~perry/maths/wildeprimes/wildeprimes.
htm

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

numbers.

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.

Richard Heylen