As two different but related infinite-length equations through analytic continuation, Hasse principle is satisfied by Riemann zeta function as a certain type of equation that generates all infinitely-many trivial zeros but this principle is not satisfied by its proxy Dirichlet eta function as a dissimilar type of equation that generates all infinitely-many nontrivial zeros. Based on two seemingly different location that are in fact identical, all nontrivial zeros are mathematically located on critical line or geometrically located on Origin point. Thus we prove location for complete Set nontrivial zeros to be critical line confirming Riemann hypothesis to be true. Sieve of Eratosthenes as a certain type of infinite-length algorithm is exactly constituted by an Arbitrarily Large Number of (self-)similar infinite-length sub-algorithms that are specified by every even Prime gaps. Modified Hasse principle is satisfied by this algorithm and its sub-algorithms that perpetually generate the Arbitrarily Large Number of all Odd Primes. Thus we prove Set even Prime gaps with corresponding Subsets Odd Primes all have cardinality Arbitrarily Large in Number confirming Modified Polignac's and Twin prime conjectures to be true.