157

Number
$157$ (one hundred and fifty-seven) is:


 * The $37$th prime number


 * The $12$th emirp after $13, 17, 31, 37, 71, 73, 79, 97, 107, 113, 149$


 * The $9$th of $29$ primes of the form $2 x^2 + 29$:
 * $2 \times 8^2 + 29 = 157$


 * The $1$st positive integer $n$ for which $\phi \left({2 n + 1}\right) < \phi \left({2 n}\right)$:
 * $\phi \left({2 \times 157 + 1}\right) = 144, \phi \left({2 \times 157}\right) = 156$


 * The largest odd positive integer that cannot be expressed as the sum of exactly $4$ non-zero square numbers all of which are coprime.


 * The $3$rd prime number after $5, 53$ which is the arithmetic mean of the prime numbers on either side of it:
 * $157 = \dfrac {151 + 163} 2$

Also see

 * Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares