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 | \(g_{\omega^{\omega2+136}}(159)\) | \(g_{\omega^{\omega10+49}12}(53)\) |