Category talk:Conjectures about prime numbers

Ok, I recall reading at around age ten or so that just like Goldbach's conjecture, it was unknown whether or not every even number is the difference of two primes. Of course this is a special case of Polignac's conjecture; but 1) is this open; 2) does this have a name and a history? Any info would be appreciated. s t r a u s s @ u a r k. e d u

Others not on Main
Others of interest:
 * 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)
 * 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)
 * there are always primes of the form k*(n-k)-1 for n>3 (AMurthy)
 * n*k + 1 is a prime for every n>1 and some k (AMurthy)

There are many many others ...--Billymac00 (talk) 15:18, 12 January 2014 (UTC)