23 Jan
2003
23 Jan
'03
6:21 a.m.
On Thu, 23 Jan 2003, Mr. Nayandeep Deka Baruah wrote:
I want a composite number n having five distinct prime factors (not repeated) such that for each prime factor p of n, p+1|n+1.
These are, as you may know, called Lucas-Carmichael numbers. The first such with n prime factors is 588455 (This may be found at http://www.users.globalnet.co.uk/~perry/maths/lucascarmichael/lucascarmichae... Using Maple I found several easily by checking products of 5 distinct primes--just using odd primes up to 100. However I didn't let the program run long before stopping it. Here's one with 6 prime factors also found in a similar manner: 206238815 = (5) (17) (23) (31) (41) (83) --Edwin