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
 
Semi and Primes 1
 
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

Semi and Primes 2

 
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

8 digit

 
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

9 digit A

 

Find 10-digit semiprimes and primes sharing this property

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Prime Numbers and tagged . Bookmark the permalink.

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.

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