Eulerchime or Echime is a number with the first 1,000 digits of Euler's number without the decimal point (including the first one).[1]. This number is also equal to \(\lfloor e\times 10^{999}\rfloor\). It's equal to:

2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427427466391932003059921817413596629043572900334295260595630738132328627943490763233829880753195251019011573834187930702154089149934884167509244761460668082264800168477411853742345442437107539077744992069551702761838606261331384583000752044933826560297606737113200709328709127443747047230696977209310141692836819025515108657463772111252389784425056953696770785449969967946864454905987931636889230098793127736178215424999229576351482208269895193668033182528869398496465105820939239829488793320362509443117301238197068416140397019837679320683282376464804295311802328782509819455815301756717361332069811250996181881593041690351598888519345807273866738589422879228499892086805825749279610484198444363463244968487560233624827041978623209002160990235304369941849146314093431738143640546253152096183690888707016768396424378140592714563549061303107208510383750510115747704171898610687396965521267154688957035035

This number is named by combining the -chime suffix with the name of Euler's number. The name was coined by Wikia user Unknown95387.

The first three prime factors of Eulerchime are 5, 10,436,037,757, and 12,478,758,287.

Approximations

Notation Lower bound Upper bound
Scientific notation \(2.718\times10^{999}\) \(2.719\times10^{999}\)
Arrow notation \(159\uparrow454\) \(115\uparrow485\)
Steinhaus-Moser Notation 386[3] 387[3]
Copy notation 2[1000] 3[1000]
Taro's multivariable Ackermann function A(3,3317) A(3,3318)
Pound-Star Notation #*((15))*19 #*((16))*19
BEAF {159,454} {115,485}
Hyper-E notation 2E999 3E999
Bashicu matrix system (0)(1)[3] (0)(1)[4]
Hyperfactorial array notation 449! 450!
Fast-growing hierarchy \(f_2(3\,308)\) \(f_2(3\,309)\)
Hardy hierarchy \(H_{\omega^2}(3\,308)\) \(H_{\omega^2}(3\,309)\)
Slow-growing hierarchy \(g_{\omega^{\omega2+136}}(159)\) \(g_{\omega^{\omega10+49}12}(53)\)

See also

Sources

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