Phi-Prime

Author

Eric W. Weisstein
February 2, 2017

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PrimeNumbers/Phi-Prime.nb.

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

©2017 Wolfram Research, Inc. except for portions noted otherwise

Code

Overlap needed because of bad behavior of V5.2 RealDigits

PhiPrime[n_]:=FromDigits[Drop[First[RealDigits[GoldenRatio,10,n+10]],-10]]

Enumeration

(p=Position[PhiPrime/@Range[1000],_?PrimeQ]//Flatten)//Timing

PhiPrime/@p

(p=Position[PhiPrime/@Range[5000],_?PrimeQ]//Flatten)//Timing

(p=Position[PhiPrime/@Range[10000],_?PrimeQ]//Flatten)//Timing

Check

A064119

l={7,13,255,280,97241};

Do[
Print[{i,l[[i]],PrimeQ[PhiPrime[l[[i]]]]//Timing}],
{i,Length[l]}
]

Floor Phi-Primes

Block[{$MaxExtraPrecision=10^6},
l=Position[Floor[GoldenRatio^Range[10^3]],_?PrimeQ]//Flatten
]//Timing

Block[{$MaxExtraPrecision=10^6},Floor[GoldenRatio^l]]

Block[{$MaxExtraPrecision=10^6},
l=Position[Floor[GoldenRatio^Range[10^4]],_?PrimeQ]//Flatten
]//Timing

Block[{$MaxExtraPrecision=10^6},
l=Position[Floor[GoldenRatio^Range[10^5]],_?PrimeQ]//Flatten
]//Timing

Ceiling Phi-Primes

Block[{$MaxExtraPrecision=10^6},l=Position[Ceiling[GoldenRatio^Range[10^3]],_?PrimeQ]//Flatten]//Timing

Block[{$MaxExtraPrecision=10^6},Ceiling[GoldenRatio^l]]

Block[{$MaxExtraPrecision=10^6},l=Position[Ceiling[GoldenRatio^Range[10^4]],_?PrimeQ]//Flatten]//Timing

Block[{$MaxExtraPrecision=10^6},l=Position[Ceiling[GoldenRatio^Range[10^5]],_?PrimeQ]//Flatten]//Timing