1,1

See comments on A153089.

Summed primes found after processing (probable) Prime[] :

2, @Prime[1]

22388562459746799685433396747, @Prime[57000046]

805356826229750685152751618123101, @Prime[384411248]

???

Currently searched to (probable) Prime[10^9] using a NTL+C program

using Miller-witness 10 trials.Checked summed primes with PrimeQ[].

Contribution from Michael J Crowe (michaelcrowe117(AT)btinternet.com), Mar 16 2009: (Start)

689400380025917209087935611674203155791, @Prime[4772152782]

3105808024815442289202546027249327480961, @Prime[6288823330]

20662615055094927265669723508498824139849, @Prime[8828698784]

(End)

Don't try this at home. lst2={}; s2=0; Do[s2=s2+Prime[n]; If[PrimeQ[s2], AppendTo[lst2, s2]], {n, 10^9}]; lst3={}; s3=0; Do[s3=s3+lst2[[n]]; If[PrimeQ[s3], AppendTo[lst3, s3]], {n, 1, Length[lst2]}]; lst3; lst4={}; s4=0; Do[s4=s4+lst3[[n]]; If[PrimeQ[s4], AppendTo[lst4, s4]], {n, 1, Length[lst3]}]; lst4; lst5={}; s5=0; Do[s5=s5+lst4[[n]]; If[PrimeQ[s5], AppendTo[lst5, s5]], {n, 1, Length[lst4]}]; lst5; lst6={}; s6=0; Do[s6=s6+lst5[[n]]; If[PrimeQ[s6], AppendTo[lst6, s6]], {n, 1, Length[lst5]}]; lst6

A000040(Level 1),A013918(Level 2),A153089(Level 3),A154422(Level 4),A154423(Level 5)

Sequence in context: A007352 A068138 A118019 this_sequence A100267 A160540 A045840

Adjacent sequences: A154421 A154422 A154423 this_sequence A154425 A154426 A154427

nonn

Michael J. Crowe (michaelcrowe117(AT)btinternet.com), Jan 09 2009

Three more terms added. Michael J Crowe (michaelcrowe117(AT)btinternet.com), Mar 16 2009