The slowest increasing sequence of primes such that no three terms sum up to a prime number.

Terms

a(0) =3a(1) =5a(2) =7a(3) =83a(4) =317a(5) =383a(6) =2111a(7) =2423a(8) =3797a(9) =8117a(10) =12143a(11) =18959a(12) =24077a(13) =33311a(14) =89561a(15) =142979a(16) =161309a(17) =191339a(18) =218531a(19) =234629a(20) =278981a(21) =297263a(22) =516911a(23) =731957a(24) =746777a(25) =882029a(26) =908627a(27) =953789a(28) =1245551a(29) =1279361