--- In

primenumbers@yahoogroups.com,

"djbroadhurst" <d.broadhurst@...> wrote:

> For similar series that demand impractical factorization, see:

> http://oeis.org/search?q=Mullin

For example,

http://oeis.org/A051334/b051334.txt
with the small seed 8191, currently leads to a

328-digit impasse, at step 60, with no conclusion

achieved in Mohsen Afshin's use of Euler-Mullin:

{mf(n)=local(f=factor(n,mp)[,1]);f[1];}

{g(m)=local(n=m+1,z,t=m,k=1);

while(!isprime(n),k++;z=mf(n);if(!isprime(z),

print("With seed "m" at step "k", C"#Str(z)" is unfactorized.");

break());t*=z;n=t+1);n;}

{help=[16293787,16639867,26945441,90670999,1340659787,

1406593120897,1193114397863177,34417238589462247,

280460690293140589,17797975387733759209,

11946702618236600549201000463124069,

54540542259000816707816058313971443];}

{mp=10^7;default(primelimit,mp);

for(k=1,#help,p=help[k];if(isprime(p),addprimes(p)));

g(8191);}

With seed 8191 at step 60, C328 is unfactorized.

David