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4 or more primes (Posted on 2019-01-03) Difficulty: 3 of 5
Find the smallest number n where n and n+1 are both
products of 4 or more primes.

See The Solution Submitted by Ady TZIDON    
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Solution computer solution | Comment 2 of 3 |

As stated, the first such pair is 80 and 81:


80 = 2*2*2*2*5

81 = 3*3*3*3


Others follow below, with the numbers followed by their counts of unique primes and all primes including duplicates:


80 2      5

81 1      4


135 2      4

136 2      4


224 2      6

225 2      4


296 2      4

297 2      4


350 3      4

351 2      4


351 2      4

352 2      6


375 2      4

376 2      4


440 3      5

441 2      4


If however we want to count only unique (that is, different) primes, the first pair is 7314 and 7315:


7314 = 2*3*23*53

7315 = 5*7*11*19


others follow:


7314 4      4

7315 4      4


8294 4      4

8295 4      4


8645 4      4

8646 4      4


9009 4      5

9010 4      4


  Posted by Charlie on 2019-01-03 12:42:41
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