**unbent@ecsvax.UUCP** (11/30/84)

==> Now what he wants to know is this: 11 and 101 are the first two primes with digit sum = 2. What's the next one? That is, what's the next prime of the form 100...001, where the ellipsis is filled out with more 0's? [I think I'll see if I can get Paul his own net logon for Christmas!] --Jay Rosenberg ...{decvax,akgua}!mcnc!ecsvax!unbent ========================================================================= Dept. of Philosophy; University of North Carolina; Chapel Hill, NC 27514 =========================================================================

**bruce@godot.UUCP (Bruce Nemnich)** (12/04/84)

I just started reading net.math again; I missed the first palindrome prime discussion. However, I dug out some prime-testing routines I had and came up with a few results this evening. Re decimal numbers with all one-digits, yes, the 19- and 23-digit ones are prime. The next in the sequence is 315 digits. Re palindrome primes, my favorite is 123456789012343210987654321. It is the only such prime < 10**261 (and probably more; that's how far my routine has crunched so far). Re primes of the form 1+10**n, I can think of no reason why there should be none (for n even, of course). Other than 101, there are none through 1+10**200. -- --Bruce Nemnich, Thinking Machines Corporation, Cambridge, MA ihnp4!godot!bruce, bjn@mit-mc.arpa ... soon to be bruce@godot.arpa

**bruce@godot.UUCP (Bruce Nemnich)** (12/04/84)

>Re decimal numbers with all one-digits, yes, the 19- and 23-digit ones >are prime. The next in the sequence is 315 digits. Oops. I meant 317, not 315. -- --Bruce Nemnich, Thinking Machines Corporation, Cambridge, MA ihnp4!godot!bruce, bjn@mit-mc.arpa ... soon to be bruce@godot.arpa

**gjk@talcott.UUCP (Greg J Kuperberg)** (12/05/84)

> Re primes of the form 1+10**n, I can think of no reason why there should > be none (for n even, of course). Other than 101, there are none through > 1+10**200. ... > --Bruce Nemnich, Thinking Machines Corporation, Cambridge, MA > ihnp4!godot!bruce, bjn@mit-mc.arpa ... soon to be bruce@godot.arpa You need only look for primes of the form 1+10**(2**n). This follows from the fact that the polynomial x**(2*n+1) can be factored. --- Greg Kuperberg harvard!talcott!gjk "Madam, there is only one important question facing us, and that is the question whether the white race will survive." -Leonid Breshnev, speaking to Margaret Thatcher.