Let $E(F_{p_n})$ is an elliptic curve defined over $GF(p_n)$ with $y^2=x^3+ax+b$,which $p_n$ is $n^{th}$ prime number. Is this clam true: for each $n>3$ there exist $a,b$ such that $\#E(F_{p_n})=p_{n+1}$?
Elliptic curves and prime numbers
Meysam Ghahramani
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