Ferrier's Prime

According to Hardy and Wright (1979), the largest Prime found before the days of electronic computers is the 44-digit number

$$F\equiv {\textstyle{1\over 17}}(2^{148}+1)=20988936657440586486151264256610222593863921,$$

which was found using only a mechanical calculator.

References

Hardy, G. H. and Wright, E. M. An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 16-22, 1979.