document.write( "Question 871159: I would appreciate help with this question please.
\n" ); document.write( "Checking to see whether the number p is prime or not.
\n" ); document.write( "Is it enough to test that p does not have any divisors ≤ square root of p.
\n" ); document.write( "
\n" ); document.write( "

Algebra.Com's Answer #525473 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "Yes because suppose p has a factor q > \"sqrt%28p%29\"\r\n" );
document.write( "\r\n" );
document.write( "and you have tried all the numbers less than \"sqrt%28p%29\". \r\n" );
document.write( "\r\n" );
document.write( "Then \"p%2Fq\" would also be a factor of p\r\n" );
document.write( "\r\n" );
document.write( "and \"p%2Fq\" < \"p%2Fsqrt%28p%29\" = \"p%2Asqrt%28p%29%2Fp\" = \"sqrt%28p%29\"\r\n" );
document.write( "\r\n" );
document.write( "so you would already have found the factor \"p%2Fq\" since it is less\r\n" );
document.write( "than \"sqrt%28p%29\" and you would have known that p was not prime.  So\r\n" );
document.write( "there would be no use to try q.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\n" ); document.write( "
\n" );