number_mersenne Number number_multiprimality

Number >> Number > number_minimumprimegap

number_minimumprimegap

Returns the number minimum prime gap.

Calling Sequence

[gap,p] = number_minimumprimegap ( n )

Parameters

n :

a 1-by-1 matrix of floating point integers, the largest prime to consider

gap :

a m-by-1 matrix of floating point integers, the difference of prime numbers

p :

a m-by-1 matrix of floating point integers, the corresponding prime number

Description

Returns the minimum prime gap function. The integer gap(k) = q-p(k), where q is the prime just greater than p(k). The integer p(k) is the smallest prime number so that the differnce of primes is gap(k).

Examples

[gap,p] = number_minimumprimegap ( 1500 )
expected_gap = [1 2 4 6 8 14 18 20 22 34]'
expected_p = [2 3 7 23 89 113 523 887 1129 1327]'

// Plot it
stacksize("max");
scf();
n=1000000;
[gap,p] = number_minimumprimegap ( n );
plot(gap,log(p)^2,"bo")
plot(gap,gap,"r-")
legend(["Empirical","Cramer-Shanks Conjecture"]);

Bibliography

http://mathworld.wolfram.com/PrimeGaps.html

Authors

number_mersenne Number number_multiprimality