Prime numbers p – DigitSum(p) = DigitProduct(p)

 

Find prime numbers for which the sum of digits equals the product of digits

 
For example,

 
4-digit prime numbers using digits:    (1, 1, 2, 4)

2141
2411
4211

1\times 1\times 2\times 4 \; = \; 8 \; = \; 1 + 1 + 2 + 4

 

5-digit prime numbers using digits:    (1, 1, 1, 2, 5)

11251
12511
15121
25111

1\times 1\times 1\times 2\times 5 \; = \; 10 \; = \; 1 + 1 + 1 + 2 + 5

 
5-digit prime numbers using digits:    (1, 1, 2, 2, 2)

21221

1\times 1\times 2\times 2\times 2 \; = \; 8 \; = \; 1 + 1 + 2 + 2 + 2

 

7-digit prime numbers using digits:    (1, 1, 1, 1, 1, 2, 7)

1112171
1127111
1172111
1271111
7112111

1\times 1\times 1\times 1\times 1\times 2\times 7 \; = \; 14 \; = \; 1 + 1 + 1 + 1 + 1 + 2 + 7

 

8-digit prime numbers using digits:    (1, 1, 1, 1, 1, 1, 2, 8)

11112811
11128111

1\times 1\times 1\times 1\times 1\times 1\times 2\times 8 \; = \; 16 \; = \; 1 + 1 + 1 + 1 + 1 + 1 + 2 + 8

 

Any 6-digit primes?

Find other 8-digit prime numbers sharing this property.

Find 9-digit primes, and larger primes.

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

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

3 Responses to Prime numbers p – DigitSum(p) = DigitProduct(p)

  1. David @InfinitelyManic says:

    I’m testing some code to resolve a rounding error issue so there could be false positives…

    p, digitSum, digitProd
    104021 8 8
    105211 10 10
    110251 10 10
    112501 10 10
    115021 10 10
    115201 10 10
    120041 8 8
    120401 8 8
    120511 10 10
    121501 10 10
    122021 8 8
    122201 8 8
    124001 8 8
    125101 10 10
    150211 10 10
    151201 10 10
    201151 10 10
    201401 8 8
    201511 10 10
    202121 8 8
    204101 8 8
    205111 10 10
    210401 8 8
    211051 10 10
    211501 10 10
    221021 8 8
    221201 8 8
    222011 8 8
    240011 8 8
    240101 8 8
    401201 8 8
    412001 8 8
    501121 10 10
    510121 10 10
    511201 10 10
    512011 10 10
    512101 10 10
    520111 10 10

  2. David @InfinitelyManic says:

    Some 8 digit primes
    I’m testing some code to resolve a rounding error issue so there could be false positives…
    p, digitSum, digitProd

    10001521 10 10
    10004201 8 8
    10010251 10 10
    10012501 10 10
    10020041 8 8
    10020151 10 10
    10020401 8 8
    10021051 10 10
    10025011 10 10
    10025101 10 10
    10042001 8 8
    10051021 10 10
    10102501 10 10
    10112171 14 14
    10121117 14 14
    10125001 10 10
    10150201 10 10
    10171121 14 14
    10171211 14 14
    10202021 8 8
    10205011 10 10
    10205101 10 10
    10211171 14 14
    10211711 14 14
    10215001 10 10
    10222001 8 8
    10400021 8 8
    10420001 8 8
    10501201 10 10
    10502101 10 10
    10520101 10 10
    10521001 10 10
    11002051 10 10
    11017211 14 14
    11020501 10 10
    11027111 14 14
    11050021 10 10
    11050201 10 10
    11101217 14 14
    11110217 14 14
    11110271 14 14
    11112811 16 16
    11117021 14 14
    11120171 14 14
    11128111 16 16
    ….

  3. David @InfinitelyManic says:

    Some 9 digit primes

    I’m testing some code to resolve a rounding error issue so there could be false positives…
    p, digitSum, digitProd

    100000421 8 8
    100001204 8 8
    100002212 8 8
    100005121 10 10
    100012116 12 12
    100016211 12 12
    100020003 6 6
    100020122 8 8
    100020212 8 8
    100020511 10 10
    100021105 10 10
    100022201 8 8
    100040201 8 8
    100041002 8 8
    100042001 8 8
    100050211 10 10
    100061121 12 12
    100102004 8 8
    100102105 10 10
    100102116 12 12
    100102202 8 8
    100106121 12 12
    100110052 10 10
    100111127 14 14
    100111721 14 14
    100112171 14 14
    100116201 12 12
    100117211 14 14
    100120116 12 12
    100120611 12 12
    100121711 14 14
    100141131 12 12
    100160211 12 12
    100171121 14 14
    100201105 10 10
    100210116 12 12
    100211117 14 14
    100250011 10 10

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