Magical primes

Probability Level 1

A magical prime is a number that is prime and has all its digits add up to a prime number. Assuming this, how many magical primes are there between 100-160?

0 7 6 5

Jonathan Tse by Jonathan Tse , 20, Hong Kong

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3 solutions

Kyle T
Jul 26, 2019 
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<?php
$c = 0;
for($i=100;$i<=160;$i++){
    if(is_prime($i)){
        $v = array_sum(str_split($i));
        if(is_prime($v)){
            echo $i.' '.$v.'<br>';
            $c++;
        }
    }
}
echo 'total: '.$c;

function is_prime($n){ 
    if ($n == 1) 
    return false; 
    for ($i = 2; $i <= $n/2; $i++){ 
        if ($n % $i == 0) 
            return false; 
    } 
    return true; 
}

/*
101 2
113 5
131 5
137 11
139 13
151 7
157 13
total: 7
*/

?>

0 Helpful 0 Interesting 0 Brilliant 0 Confused

101, 113, 131, 137, 139, 151 and 157

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Jonathan Tse
May 29, 2019

These are all the primes from 100-160:

101 103 107 109 113 127 131 137 139 149 151 157

Only 101, 113, 131, 137, 139, 151, 157 are magical primes.

So there are 7 magical primes from 100-160

0 Helpful 0 Interesting 0 Brilliant 0 Confused

These are apparently known as "additive primes". More info at OEIS here .

Chris Lewis - 2 years ago

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