83

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Number

$83$ (eighty-three) is:

The $23$rd prime number

The $7$th safe prime after $5$, $7$, $11$, $23$, $47$, $59$:

$83 = 2 \times 41 + 1$

The $7$th of $11$ primes of the form $2 x^2 + 11$:

$2 \times 6^2 + 11 = 83$ (Previous  ... Next)

The $9$th Sophie Germain prime after $2$, $3$, $5$, $11$, $23$, $29$, $41$, $53$:

$2 \times 83 + 1 = 167$, which is prime.

The $14$th prime $p$ after $11$, $23$, $29$, $37$, $41$, $43$, $47$, $53$, $59$, $67$, $71$, $73$, $79$ such that the Mersenne number $2^p - 1$ is composite

The $14$th left-truncatable prime after $2$, $3$, $5$, $7$, $13$, $17$, $23$, $37$, $43$, $47$, $53$, $67$, $73$

The $33$rd odd positive integer that cannot be expressed as the sum of exactly $4$ distinct non-zero square numbers all of which are coprime

$1$, $\ldots$, $37$, $41$, $43$, $45$, $47$, $49$, $53$, $55$, $59$, $61$, $67$, $69$, $73$, $77$, $83$, $\ldots$

Also see

• Previous  ... Next: Sophie Germain Prime
• Previous  ... Next: Safe Prime
• Previous  ... Next: Left-Truncatable Prime
• Previous  ... Next: Odd Numbers Not Expressible as Sum of 4 Distinct Non-Zero Coprime Squares
• Previous  ... Next: Prime Number
• Previous  ... Next: Sequence of Indices of Composite Mersenne Numbers