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Results tagged with prime-numbers
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user 8140
Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.
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Conjecture:if $i<j$,then $\pi(p[i]+i)-i<=\pi(p[j]+j)-j+1$
p[i] is the i-th prime. $\pi(x)$ is prime counting function.
Firstly, I think that this Prime gap inequality holds true,
$ p[i+1] - p[i] <= i $
Prove:for any i>0, we can always find distinct prime …
- 217
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A prime sequence can be partitioned into two sets of equal or consecutive sum
Denote $P[n]$ as the prime sequence $\{p_1,p_2,\cdots,p_n\}$.
Conjecture:
When $n=2k+1$ is odd, prime list $P[n]$ can be partitioned into two non-overlapping sublists, in which each sublist has equ …
- 217