Percents of primes

Number Theory Level 2

What percent of numbers between $0$ and $100$ which end with a $1$ are prime?

50% 40% 60% 70%

2 solutions

David Stiff
Apr 28, 2018

There are $10$ numbers between $0$ and $100$ which end with a $1$ :

$1, 11, 21, 31, 41, 51, 61, 71, 81, 91$

Five of these are prime:

$11, 31, 41, 61, 71$

Thus, if $5$ out of $10$ of the numbers are prime, $\frac{1}{2}$ of the numbers, or $\boxed{50\%}$ are prime.

Giorgos K.
Apr 29, 2018

Here is a $Mathematica$ code in order to compute bigger intervals (just change the "Range" value)

N@Length@Select[s=Select[Range@100,Last@IntegerDigits@#==1&],PrimeQ]/Length@s