sentences:  For example, the AP-3 with primes {3, 5, 7} and common difference 2# = 2, or the AP-5 with primes {5, 11, 17, 23, 29} and common difference 4# = 6.It is conjectured that such examples exist for all primes "k"., the largest prime for which this is confirmed is "k" = 19, for this AP-19 found by Wojciech Iżykowski in 2013