The largest Fibonacci prime currently known as of March 2017 is F104,911, where F1 = F2 = 1. It is 21,925 digits long and was discovered in October 2015.[1]

The largest known Fibonacci prime candidate is F3,340,367, which is 698,096 digits long. It was discovered in March 2018.[2]

Approximations

Notation Approximation
Scientific notation \(5.66\times10^{21\,924}\)
Arrow notation \(2\uparrow\uparrow5\)
BEAF \(\{2,5,2\}\)
Chained arrow notation \(2\rightarrow5\rightarrow2\)
Multivariable Ackermann \(Ack(4,2)\)
Fast-growing hierarchy \(f_2(f_2(13))\)

Sources

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