例题讲解2 1 7.以 Sn 表示前 n个质数之和 :S1=2 ,S2 =2 + 3=5 ,S3=2 + 3+ 5 =1 0 ,…求证 :对每个自然数 n,在 Sn 和 Sn+1之间必有一个完全平方数 .证明　因为任意两个奇质数之差不小于2 ,故我们只需证明下面更一般的命题 :“设数列 {an}满足 :a1=2 ,a2 =3,an+1- an ≥ 2(n =2 Example to explain 2 1 7. Express the sum of the first n prime numbers with Sn: S1=2, S2 =2 + 3=5, S3=2 + 3+ 5 =1 0,... Prove: For each natural number n, in Sn There must be a complete square number between Sn and +1. Prove that because the difference between any two odd prime numbers is not less than 2, we only need to prove the following more general proposition: "Set the number column {an} to satisfy: a1=2, a2 =3,an+1- an ≥ 2(n = 2