We denote by {p 1 =2, p 2 =3, p 3 =5,..., p k ,...} the sequence of increasing primes, and for each positive integer k≥1 let S(k):=min{2n>p k : 2n.p 1 , 2n.p 2 ,..., 2n.p k all are composite numbers }. We prove that the following conjectures are equivalent to the Goldbach's conjecture. Conjecture B. For every positive integer k , we have S(k) ≥ p k+ 1 + 3. Conjecture C. For every positive integer k , the number S(k) is the sum of two odd primes.
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机译：我们用{p 1 = 2，p 2 = 3，p 3 = 5，...，pk，...}表示递增质数的序列，对于每个k≥1的正整数，令S（k）：= min {2n> pk：2n.p 1，2n.p 2，...，2n.pk都是复合数字}。我们证明以下猜想等同于哥德巴赫猜想。猜想B。对于每个正整数k，我们有S（k）≥p k + 1 +3。猜想C。对于每个正整数k，数S（k）是两个奇数质数之和。
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