85

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Number

$85$ (eighty-five) is:

$5 \times 17$

The $2$nd Fermat pseudoprime to base $4$ after $15$:

$4^{85} \equiv 4 \pmod {85}$

The $3$rd positive integer after $50$, $65$ which can be expressed as the sum of two square numbers in two or more different ways:

$85 = 9^2 + 2^2 = 7^2 + 6^2$

The $4$th non-square positive integer which cannot be expressed as the sum of a square and a prime:

$10$, $34$, $58$, $85$, $\ldots$

The $5$th Smith number after $4$, $22$, $27$, $58$:

$8 + 5 = 5 + 1 + 7 = 13$

The $7$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $85$, $\ldots$

The $10$th positive integer $n$ after $0$, $1$, $5$, $25$, $29$, $41$, $49$, $61$, $65$ such that the Fibonacci number $F_n$ ends in $n$

The $16$th positive integer $n$ after $5$, $11$, $17$, $23$, $29$, $30$, $36$, $42$, $48$, $54$, $60$, $61$, $67$, $73$, $79$ such that no factorial of an integer can end with $n$ zeroes

The $27$th semiprime:

$85 = 5 \times 17$

Also see

• Previous  ... Next: Fermat Pseudoprime to Base 4
• Previous  ... Next: Non-Square Positive Integers not Sum of Square and Prime
• Previous  ... Next: Smith Number
• Previous  ... Next: Numbers not Sum of Square and Prime
• Previous  ... Next: Sequence of Fibonacci Numbers ending in Index
• Previous  ... Next: Sum of 2 Squares in 2 Distinct Ways
• Previous  ... Next: Numbers of Zeroes that Factorial does not end with
• Previous  ... Next: Semiprime Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $85$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $85$