DanA> I'm curious: Can one state in closed form what is the asymptotic density of prime numbers among numbers Q(n) of the form Q(n) := primorial(n) + 1 i.e., Q(n) = 2*3*5*7*...*p_n + 1 (where p_n is the nth prime) ??? CG>It's not even known that there are infinitely many. Caldwell & Gallot conjecture that there are about e^gamma * log x prime Q(n) with n <= x, that is, that the usual heuristic gives the right answer. I think sieve theory can give an upper bound if that's enough for your purposes. Charles Greathouse WDS>--I would think that Q(n) is prime with "probability" about loglog(Q(n)) times greater than the usual 1/log(Q(n)) probability. [Warren] Only slightly less infeasible might be the coprime sequence A000058 (interesting comments). In[10]:= NestList[#^2 - # + 1 &, 2, 9] Out[10]= {2, 3, 7, 43, 1807, 3263443, 10650056950807, 113423713055421844361000443, 12864938683278671740537145998360961546653259485195807, 165506647324519964198468195444439180017513152706377497841851388766535868639572406808911988131737645185443} In[8]:= N[Timing[Nest[#^2 - # + 1 &, 2, 21]]] Out[8]= {0.007302, 1.853733657356281*10^426880} (Half a million digits in 7ms?) In[6]:= TimeConstrained[PrimeQ[#], 1] & /@ NestList[#^2 - # + 1 &, 2, 21] Out[6]= {True, True, True, True, False, True, False, False, False, False, False, False, False, False, False, False, False, False, $Aborted, $Aborted, False, $Aborted} where $Aborted almost certainly means True. Changing the timeout from 1 to 288 sec did zilch. Decertifying a_20 In[9]:= Timing[PrimeQ[Nest[#^2 - # + 1 &, 2, 20]]] Out[9]= {0.150525, False} took < 1/6 sec. Can we show there are no (strong?) pseudoprimes of this form? --rwg SUPERIMPOSED PSEUDOPRIMES