251

Number
$251$ (two hundred and fifty-one) is:


 * The $54$th prime number.


 * The $1$st positive integer which can be expressed as the sum of $3$ cubes numbers in two or more different ways:
 * $251 = 5^3 + 5^3 + 1^3 = 6^3 + 3^3 + 2^3$


 * The larger of the $3$rd pair of primes whose prime gap is $10$:
 * $251 - 241 = 10$


 * The $4$th obstinate number after $1$, $127$, $149$


 * The $15$th trimorphic number after $1$, $4$, $5$, $6$, $9$, $24$, $25$, $49$, $51$, $75$, $76$, $99$, $125$, $249$:
 * $251^3 = 15 \, 813 \, \mathbf {251}$


 * The $18$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$, $83$, $89$, $113$, $131$, $173$, $179$, $191$, $233$, $239$:
 * $2 \times 251 + 1 = 503$, which is prime.


 * The $23$rd minimal prime base $10$ after $11$, $13$, $17$, $19$, $23$, $29$, $31$, $37$, $41$, $43$, $47$, $53$, $59$, $61$, $67$, $71$, $73$, $79$, $83$, $89$, $97$, $227$

Also see