Belphegor's prime

Belphegor's prime is the name for the number 1,000,000,000,000,066,600,000,000,000,001 = \(10^{30} + 666 \cdot 10^{14} + 1\).Clifford Pickover, Belphegor's Prime: 1000000000000066600000000000001! It is a palindromic prime, notable for its curious decimal expansion containing the beast number. named the number after a from the Judeo-Christian mythos, playing on 666's association with the devil in numerology.
In terms of digit repetition, the number could be written \(1\underbrace{000\ldots000}_{13}666\underbrace{000\ldots000}_{13}1\). (The presence of the number 13 — associated with in Western culture — further ties into the numerological theme.)
The Belphegor's primes may also be defined as prime numbers of the form
\[B_n = 10^{2n+4} + 666 \cdot 10^{n+1} + 1 = 1\underbrace{000\ldots000}_n666\underbrace{000\ldots000}_n1\]
and the first few Belphegor's primes are \(B_n\) for \(n = 0,\,13,\,42,\,506,\,608,\,2472,\,2623,\,28291,\,181298\).MathWorld, Belphegor PrimeOEIS A232448
== Approximations ==
Notation 	Lower bound 	Upper bound
Scientific notation 	\(1\times10^{30}\) 	\(1.001\times10^{30}\)
Arrow notation 	\(10\uparrow30\) 	\(75\uparrow16\)
Steinhaus-Moser Notation 	22[3] 	23[3]
Copy notation 	9[30] 	1[31]
Taro's multivariable Ackermann function	A(3,96) 	A(3,97)
Pound-Star Notation 	#*(9,6,4)*9 	#*(0,1,0,0,1)*5
BEAF 	{10,30} 	{75,16}
Hyper-E notation 	E30 	E[75]16
Bashicu matrix system 	(0)(0)(0)[5623] 	(0)(0)(0)[5624]
Hyperfactorial array notation 	28! 	29!
Fast-growing hierarchy 	\(f_2(93)\) 	\(f_2(94)\)
Hardy hierarchy 	\(H_{\omega^2}(93)\) 	\(H_{\omega^2}(94)\)
Slow-growing hierarchy 	\(g_{\omega^{\omega3}}(10)\)	\(g_{\omega^{\omega+8}12+\omega^{\omega+7}10}(16)\)
== Sources ==
== See also ==
Category:Numbers
Category:Prime numbers
Category:Class 2
Category:Numbers with 30 to 100 digits
ja:ベルフェゴール素数