nextprime

This is actually a tool in my vpi toolbox, but it works quite nicely on any number. As such, I decided it would make sense to submit the function also separately.

tic,nextprime(1000000000),toc
ans =
1000000007
Elapsed time is 0.006276 seconds.

A partial sieve scheme is used to avoid testing the primality of too many numbers. This makes it more efficient.

You can use it on lists of numbers too.

nextprime(1000:100:2000)
ans =
1009 1103 1201 1301 1409 1511 1601 1709 1801 1901 2003

You can search in either direction, above or below the starting point too.

nextprime(43420000,'above')
ans =
43420007

nextprime(43420000,'below')
ans =
43419977

The limit for nextprime when applied to double precision numbers is now 2^46. Thus you cannot find the next prime above 2^46, unless you are working with vpi numbers.

>> nextprime(2^47)
??? Error using ==> nextprime at 89
The maximum value of N (for numeric input) allowed is 2^46.

Instead, apply nextprime to any integer or set thereof as vpi numbers. This works perfectly, but you will need to install my vpi toolbox.

>> nextprime(vpi(2).^[12;47;53;86])
ans =
4099
140737488355333
9007199254740997
77371252455336267181195291