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Talk:Conjectures

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Idea

Perhaps links and/or pages on subsets can be made. One might be conjectures for prime numbers. Besides the very famous (GC,TP), it might include a partial list of conjectures specific to prime numbers:

  • every prime n>5 = a prime plus prod of 2 consecutive integers (Zhi-Wei Sun)
  • For any even number 2*n > 0, 2*n + sigma(k) is prime for some 0 < k < 2*n (Zhi-Wei Sun)
  • every odd n>5 = p+2q where p,q are primes (see A046927) (Lemoine)
  • every sufficiently large odd integer N can be partitioned as the sum of three primes (Goldbach-Vinogradov)
  • for any integer n>0, the difference between the primorial n# and the nearest prime number above (excluding the possible primorial prime n#+1) is always a prime number (Fortune)
  • three times any odd square not divisible by 5 is a sum of squares of three primes other than 2 and 3 (regarding 1 as a prime) (Catalan)
  • there is always a prime between n^2 and (n+1)^2 (Legendre)
  • there are always primes of the form k*(n-k)-1 for n>3 (AMurthy, A109909)
  • n*k + 1 is a prime for every n>1 and some k (AMurthy, A034693)
  • every odd integer exceeding 3 is either a prime number or the sum of three prime numbers (Waring)

--Bill McEachen 18:45, 12 January 2014 (UTC)

Well, there is a page List of prime conjectures. I've added a link to the See Also section. Alonso del Arte 04:17, 13 January 2014 (UTC)
Here's a partial concordance to conjectures in the OEIS: Talk:Conjectures/List. As far as narrowing it down... that seems hard, there are almost 2000 here. Charles R Greathouse IV 04:43, 13 January 2014 (UTC)
At least one or two among those are actually resolved. I found Gary's second conjecture in A008364 rather surprising, because it seems like one of those easy exercises you might find among the first few study problems in the chapter on congruences in a textbook. Alonso del Arte 05:18, 13 January 2014 (UTC)