An emirp is a prime number which is prime both forwards and backwards. The largest known emirp to date is \(10^{10,006}+{941992101\times 10^{4,999}}+1\).[1]

It is an extremely easy to memorize number, as it is comprised of almost all zeroes with 1's on either side and a short number in between. The number of digits of this number is also an emirp, as both 10,007 and 70,001 are prime.

The largest known emirp is equal to about \(f_{2}(33\,224)\) in the fast-growing hierarchy.

Decimal expansion

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0000001

Approximations

Notation Lower bound Upper bound
Scientific notation \(1\times10^{10,006}\) \(1.001\times10^{10,006}\)
Arrow notation \(10\uparrow10,006\) \(1871\uparrow3,058\)
Steinhaus-Moser Notation 2891[3] 2892[3]
Copy notation 9[10006] 1[10007]
Taro's multivariable Ackermann function A(3,33236) A(3,33237)
Pound-Star Notation #*((21))*52 #*((22))*52
BEAF {10,10006} {1871,3058}
Hyper-E notation E10006 2E10006
Bashicu matrix system (0)(1)[3] (0)(1)[4]
Hyperfactorial array notation 3,250! 3,251!
Fast-growing hierarchy \(f_2(33\,224)\) \(f_2(33\,225)\)
Hardy hierarchy \(H_{\omega^2}(33\,224)\) \(H_{\omega^2}(33\,225)\)
Slow-growing hierarchy \(g_{\omega^{\omega^4+6}}(10)\) \(g_{\omega^{\omega\times52+55}30}(96)\)

Sources

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