Talk:Chernick's Carmichael numbers

Does anyone know whether a(10) actually exists?

I've checked all values of 'm' up to 16 billion and found nothing. This is in contrast to a(9) which only required 'm' equal to 950,560.

So, if a(10) does exist, it must be very large and, given the nature of the constraints, the probability of finding 10 primes which satisfy them is beginning to look low to me. --PureFox (talk) 18:48, 3 June 2019 (UTC)

a(10) was discovered today by Amiram Eldar (the author of the A318646 sequence) for m = 3208386195840. -- Trizen (talk) 12:10, 4 June 2019 (UTC)

Yep, knowing that, I've now found a(10) to be:

24616075028246330441656912428380582403261346369700917629170235674289719437963233744091978433592331048416482649086961226304033068172880278517841921

So my 16 billion wasn't even in the right ballpark and I estimate it would have taken my Go program about 8.5 days to find it, albeit on slow hardware. On a fast machine, using a faster compiler and GMP for the big integer stuff, you might be able to get this down to a few hours but it's probably best to remove it as an optional requirement as I see you've now down. Interesting task nonetheless so thanks for creating it. --PureFox (talk) 15:03, 4 June 2019 (UTC)