Pari/GP code to print out any large prime numbers encountered during calculation of recursive prime predecessor notation. The largest prime factor (even if it is raised to a power) is never printed though it is recursively analyzed.
f1(x)=my(n,m,r,p); n=factorint(x); m=matsize(n); for(r=1,m[1], p=n[r,1]; if(r!=m[1]&&p>10^10,print(p)); if(p!=2,f1((p-1)/2)))
Applied to the 10th Sylvester number:
21430986826194127130578627950810640891005487
17771487413
344079096271707611
1068023221302870183851176062588287
135388757627
546878507865802279
145904345518894913
These numbers can be added to addprimes
to make future computations faster.
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