Mills' Prime

Author

Eric W. Weisstein
July 25, 2013

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/MillsPrime.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/MillsPrime.html.

©2013 Wolfram Research, Inc. except for portions noted otherwise

Sequences

A108739

offsets={3,30,6,80,12,450,894,3636,70756,97220,66768,300840};
b[n_]:=offsets[[n]]
f[1]:=2
f[n_]:=f[n]=f[n-1]^3+b[n-1]

Values

NestList[NextPrime[#^3]&,2,7]//Timing

f/@Range[8]

IntegerLength/@(f/@Range[13])

<<Utilities`EISFormat`

BFile["a051254.txt",f/@Range[13]]

Primality Check

{$MachineName,$TopDirectory,DateString[],$Version}//Column

Do[
Print[{n,IntegerLength[f[n]],PrimeQ[f[n]]//Timing}],
{n,Length[offsets]+1}]

b-terms

(Subscript[b, 11])

b[11]//N

b11one=((((((2521008887^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220;

b11two=(((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220;

b11one==b11two

b11one==b[11]

(Subscript[b, 13])

b[13]//N

b13=(((((((((((2^3+3)^3+30)^3+6)^3+80)^3+12)^3+450)^3+894)^3+3636)^3+70756)^3+97220)^3+66768)^3+300840;

b13==b[13]