### About the Number 523 (five hundred twenty-three)

MathBabbler finished processing a box of 523 pencils on 13 December 2014.

```MathBabbler Number Analyst (MBNA) output:
=========================================
523 is a natural, whole, integer
523 is odd
523 proper divisors are: 1,
523 has 1 proper divisors
523 is deficient (sum of divisors is 1; ratio: 0.00191205)
523 is unhappy
523 is a Squarefree Number
523 is prime (not composite)
...Twin prime with 521
...OEIS:002145 (4n+3; n=130)
...Left-truncatable
523 is the sum of 7 consecutive primes
523 = 61 + 67 + 71 + 73 + 79 + 83 + 89
523 in octal is 01013
523 in hexadecimal is 0x20b
523 in binary is 1000001011 (is evil)
523 nearest square numbers: -39...6 (484...529 [23])
sqrt(523) = 22.8692
ln(523) = 6.25958
log(523) = 2.7185
523 reciprocal is .00191204588910133843212237093690
523! is 2.50484e+1196
523 is 166.476 Pi years
523 is 26 score and 3 years
523 written as a Roman numeral is DXXIII
523 is 262^2 - 261^2 and 262 + 261 = 523
```

`log10(523)` - e = 0.000219860408229. In other words, the common logarithm of `523` provides a good approximation of the mathematical constant e.

Creator: Gerald Thurman [gthurman@gmail.com]
Created: 13 December 2014 (posted 14 December 2014)