Primes at the upper end of the gaps mentioned in A144104.

Terms

a(0) =3a(1) =5a(2) =11a(3) =17a(4) =29a(5) =37a(6) =53a(7) =59a(8) =127a(9) =149a(10) =211a(11) =223a(12) =307a(13) =331a(14) =541a(15) =1361a(16) =1693a(17) =1973a(18) =2203a(19) =2503a(20) =2999a(21) =3299a(22) =4327a(23) =4861a(24) =5623a(25) =5779a(26) =5981a(27) =6521a(28) =6947a(29) =7283