## Prime numbers & semiprimes : DigitSum(p) = DigitProduct(p)

To find prime numbers and semiprimes for which the sum of digits equals the product of digits.

2-digit number :       $2\times 2 = 4 = 2 + 2$

3-digit numbers :       $1\times 2\times 3 = 6 = 1 + 2 + 3$

4-digit numbers :       $1\times 1\times 2\times 4 = 8 = 1 + 1 + 2 + 4$

5-digit numbers :
$1\times 1\times 2\times 2\times 2 = 8 = 1 + 1 + 2 + 2 + 2$
$1\times 1\times 1\times 2\times 5 = 10 = 1 + 1 + 1 + 2 + 5$

6-digit numbers :
$1\times 1\times 1\times 1\times 2\times 6 = 12 = 1 + 1 + 1 + 1 + 2 + 6$

7-digit numbers :
$1\times 1\times 1\times 1\times 1\times 4\times 3 = 12 = 1 + 1 + 1 + 1 + 1 + 4 + 3$
$1\times 1\times 1\times 1\times 1\times 2\times 7 = 14 = 1 + 1 + 1 + 1 + 1 + 2 + 7$

8-digit numbers :
$1\times 1\times 1\times 1\times 1\times 1\times 2\times 8 = 16 = 1 + 1 + 1 + 1 + 1 + 1 + 2 + 8$
$1\times 1\times 1\times 1\times 1\times 2\times 2\times 3 = 12 = 1 + 1 + 1 + 1 + 1 + 2 + 2 + 3$

9-digit numbers :
$1\times 1\times 1\times 1\times 1\times 1\times 1\times 3\times 5 = 15 = 1 + 1 + 1 + 1 + 1 + 1 + 1 + 3 + 5$

Find 10-digit semiprimes and primes sharing this property

math grad - Interest: Number theory
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### One Response to Prime numbers & semiprimes : DigitSum(p) = DigitProduct(p)

1. K.D. BAJPAI says:

10-digit numbers :

Prime:
1111411141: 1*1*1*1*4*1*1*1*4*1 = 16 =1+1+1+1+4+1+1+1+4+1
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
Semiprimes:
1111114141 = 1231 * 902611
1111141411 = 859 * 1293529
1111414111 = 89 * 12487799
1114114111 = 11 * 101283101
1411111141 = 11 * 128282831
1411111411 = 23869 * 59119

I could not find more 10-digit primes of this form.