n^2+3n+1的值不一定都是質(zhì)數(shù)
當(dāng)n=5*m+1時(shí)(m為正整數(shù)) n^2+3n+1的值就不是質(zhì)數(shù)
n^2+3n+1
=(5*m+1)^2+3*(5*m+1)+1
=25*m^2+10*m+1+15*m+3+1
=25*m^2+25*m+5
=5*(5*m^2+5*m+1)
當(dāng)m=1時(shí)
n=5*1+1=6
n^2+3*n+1=36+18+1=55=5*11
當(dāng)m=2時(shí)
n=5*2+1=11
n^2+3*n+1=121+33+1=155=5*31
當(dāng)m=3時(shí)
n=5*3+1=16
n^2+3*n+1=256+48+1=305=5*61
……
以下情況也不是質(zhì)數(shù)
n n^2+3*n+1 \x09m1*m2
13 209 =11*19
17 341 =11*31
22 551 =19*29
24 649 =11*59
28 869 =11*79