Goldbach’s conjecture in arithmetic progressions: number and size of exceptional prime moduli
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DOI: 10.1007/s00013-016-0993-0
Abstract: Set $${T=N^{\frac{1}{3}-\epsilon}}$$T=N13-ϵ. It is proved that for all but $${\ll TL^{-H},\,H > 0}$$≪TL-H,H>0, exceptional prime numbers $${k\leq T}$$k≤T and almost all integers b1, b2 co-prime to k, almost all integers $${n\sim N}$$n∼N satisfying $${n\equiv b_{1}+b_{2}(mod\,k)}$$n≡b1+b2(modk)… read more here.
Keywords: progressions number; number size; conjecture arithmetic; exceptional prime ... See more keywords
DIGITALLY RESTRICTED SETS AND THE GOLDBACH CONJECTURE
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DOI: 10.1017/s0004972724001096
Abstract: Abstract We show that for any set D of at least two digits in a given base b, almost all even integers taking digits only in D when written in base b satisfy the Goldbach… read more here.
Keywords: sets goldbach; conjecture; goldbach conjecture; digitally restricted ... See more keywords