107

Previous  ... Next

Number

$107$ (one hundred and seven) is:

The $28$th prime number

The $3$rd of the $1$st ordered triple of consecutive integers that have Euler $\phi$ values which are strictly increasing:

$\map \phi {105} = 48$, $\map \phi {106} = 52$, $\map \phi {107} = 106$

The $4$th prime number after $53, 71, 103$ which cannot be expressed as either the sum of or the difference between a power of $2$ and a power of $3$.

The $4$th of the $2$nd ordered quadruple of consecutive integers that have divisor sums which are strictly decreasing:

$\map {\sigma_1} {104} = 210, \ \map {\sigma_1} {105} = 192, \ \map {\sigma_1} {106} = 162, \ \map {\sigma_1} {107} = 108$

The $8$th safe prime after $5$, $7$, $11$, $23$, $47$, $59$, $83$:

$107 = 2 \times 53 + 1$

The $9$th emirp after $13$, $17$, $31$, $37$, $71$, $73$, $79$, $97$

The smaller of the $10$th pair of twin primes, with $109$

The index of the $11$th Mersenne prime after $2$, $3$, $5$, $7$, $13$, $17$, $19$, $31$, $61$, $89$:

$M_{107} = 2^{107} - 1 = 162 \, 259 \, 276 \, 829 \, 213 \, 363 \, 391 \, 578 \, 010 \, 288 \, 127$

The $52$nd positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $77$, $80$, $81$, $84$, $89$, $94$, $95$, $96$, $100$, $101$, $102$ which cannot be expressed as the sum of distinct pentagonal numbers.

Also see

• Previous  ... Next: Safe Prime
• Previous  ... Next: Index of Mersenne Prime
• Previous  ... Next: Emirp
• Previous  ... Next: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
• Previous  ... Next: Prime Number
• Previous  ... Next: Twin Primes
• Previous  ... Next: Primes not Sum of or Difference between Powers of 2 and 3
• Previous  ... Next: Sequences of 3 Consecutive Integers with Rising Phi

• Previous: Sequences of 4 Consecutive Integers with Falling Divisor Sum