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This paper continues the author's previous studies on continued fractions andHeron's algorithm, as from his former JMM2017 presentation (see\cite{CF.HA}).\par\medskip Extending the notion of continued fraction to the$p$-adic fields, one can find continued fractions which converge in both realand $p$-adic topologies to the `same' quadratic irrational number, some ofwhich are given by the Heron's algorithm using a generalized version of anauthor's theorem from the cited JMM presentation. The definition can bepossibly generalized to other global fields, as left as an open question. Wewill end the part on hybrid convergence with many numerical examples. Afterthat, we will recall the basic algorithms on the $p$-adic fields studied by theauthor and see some applications of theirs to computer science: applyingHeron's algorithm to quickly compute $p$-adic square roots, finding newelementary cryptography procedures and some methods to get pseudo-randomnumbers, calculate last digits of some peculiar very big numbers.

Hybrid Continued Fractions and $n$-adic algorithms, with applications to cryptography and "unimaginable' numbers