181

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Number

$181$ (one hundred and eighty-one) is:

The $42$nd prime number

The smaller of the $2$nd pair of primes whose prime gap is $10$:

$191 - 181 = 10$

The $5$th near-repdigit prime after $101$, $113$, $131$, $151$

The $5$th and final positive integer solution after $1$, $3$, $5$, $11$ to the Ramanujan-Nagell equation $x^2 + 7 = 2^n$ for integral $n$:

$181^2 + 7 = 32 \, 768 = 2^{15}$

The $9$th palindromic prime:

$2$, $3$, $5$, $7$, $11$, $101$, $131$, $151$, $181$, $\ldots$

The $12$th prime number after $53$, $71$, $103$, $107$, $109$, $149$, $151$, $157$, $163$, $167$, $173$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$

The larger of the $13$th pair of twin primes, with $179$

The $16$th long period prime after $7$, $17$, $19$, $23$, $29$, $47$, $59$, $61$, $97$, $109$, $113$, $131$, $149$, $167$, $179$

Also see

• Previous: Solutions of Ramanujan-Nagell Equation

• Previous  ... Next: Prime Gaps of 10

• Previous  ... Next: Near-Repdigit Prime
• Previous  ... Next: Palindromic Prime

• Previous  ... Next: Primes not Sum of or Difference between Powers of 2 and 3

• Previous  ... Next: Prime Number
• Previous  ... Next: Twin Primes
• Previous  ... Next: Long Period Prime