There appear to be at least n primes in the range (x-sqrt(x), x] for all x >= a(n).

Terms

a(0) =127a(1) =1367a(2) =2531a(3) =2539a(4) =6007a(5) =7457a(6) =10061a(7) =10847a(8) =23531a(9) =35797a(10) =35801a(11) =38557a(12) =44497a(13) =47111a(14) =69767a(15) =69809a(16) =88321a(17) =107687a(18) =110419a(19) =110431a(20) =113723a(21) =127217a(22) =250673a(23) =250681a(24) =250687a(25) =250703a(26) =268487a(27) =268493a(28) =286381a(29) =286393