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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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## 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 $$g_{\omega^{\omega^4+6}}(10)$$ $$g_{\omega^{\omega\times52+55}30}(96)$$

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