# Solution of;
# Project Euler Problem 574: Verifying Primes
# https://projecteuler.net/problem=574
# 
# Let $q$ be a prime and $A \ge B >0$ be two integers with the following 
# properties: $A$ and $B$ have no prime factor in common, that is 
# $\text{gcd}(A,B)=1$. The product $AB$ is divisible by every prime less than 
# q. It can be shown that, given these conditions, any sum $A+B<q^2$ and any 
# difference $1<A-B<q^2$ has to be a prime number. Thus you can verify that a 
# number $p$ is prime by showing that either $p=A+B<q^2$ or $p=A-B<q^2$ for 
# some $A,B,q$ fulfilling the conditions listed above. Let $V(p)$ be the 
# smallest possible value of $A$ in any sum $p=A+B$ and any difference 
# $p=A-B$, that verifies $p$ being prime. Examples:$V(2)=1$, since $2=1+1< 
# 2^2$. $V(37)=22$, since $37=22+15=2 \cdot 11+3 \cdot 5< 7^2$ is the 
# associated sum with the smallest possible $A$. $V(151)=165$ since 
# $151=165-14=3 \cdot 5 \cdot 11 - 2 \cdot 7<13^2$ is the associated 
# difference with the smallest possible $A$. Let $S(n)$ be the sum of $V(p)$ 
# for all primes $p<n$. For example, $S(10)=10$ and $S(200)=7177$. Find 
# $S(3800)$.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 574
    timed.caller(dummy, n, i, prob_id)
