Ferrier's prime is \((2^{148}+1)/17 = 20,988,936,657,440,586,486,151,264,256,610,222,593,863,921\).[1][2] Discovered by Aimé Ferrier in 1951, it was the largest known prime at the time of discovery.[3]


Notation Lower bound Upper bound
Scientific notation \(2.098\times10^{43}\) \(2.099\times10^{43}\)
Arrow notation \(54\uparrow25\) \(5\uparrow62\)
Steinhaus-Moser Notation 29[3] 30[3]
Copy notation 1[44] 2[44]
Taro's multivariable Ackermann function A(3,140) A(3,141)
Pound-Star Notation #*(2,1,3,3)*9 #*(5,0,6,3,5)*6
BEAF {54,25} {5,62}
Hyper-E notation 2E43 E[5]62
Bashicu matrix system (0)(0)(0)(0)[510] (0)(0)(0)(0)[511]
Hyperfactorial array notation 37! 38!
Fast-growing hierarchy \(f_2(136)\) \(f_2(137)\)
Hardy hierarchy \(H_{\omega^2}(136)\) \(H_{\omega^2}(137)\)
Slow-growing hierarchy \(g_{\omega^{\omega2+3}15}(16)\) \(g_{\omega^{24}10}(58)\)


  1. Hardy, G. H. and Wright, E. M. (1979) An Introduction to the Theory of Numbers, 5th ed. Oxford, England: Clarendon Press, pp. 16-22.
  2. Weisstein, E. W. Ferrier's Prime MathWorld - A Wolfram Web Resource.
  3. The Largest Known Prime by Year: A Brief History. Retrieved 2017-11-04.
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