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[ January 16, 2014 ]
Gathering prime factors of nine- and pandigitals
and extracting statistical information from the data.


How many different primes divide all the ninedigitals ?
How many different primes divide all the pandigitals ?
(each digit from set [1-9] or [0-9] appears just once)

What is the largest prime factor in each case ?

What prime factor(s) has the least frequency of appearing ?

How many palindromic prime factors are there in each case ?

List of smallest and largest nine-/pandigital 9*semiprimes ?

To start with I give the smallest and largest nine- and pandigital
prime factorizations.

123456789 = 32 x 3607 x 3803

987654321 = 32 x 172 x 379721

yielding already this subset {... ,3,...,17,...,3607,...,3803,...,379721,... }

and

1023456789 = 34 x 2221 x 5689

9876543210 = 2 x 32 x 5 x 172 x 379721

yielding already this subset {2,3,5,...,17,...,2221,...,5689,...,379721,... }

The rest is up to you. Good luck.


Some related sources

A178775 Smallest prime factors of zerofull restricted pandigital numbers.
A204532 Largest prime factors of zerofull restricted pandigital numbers A050278.

A216203 Smallest prime that does not divide at least one n-digit zeroless pandigital number.
A228253 Smallest prime that does not divide at least one n-digit pandigital number.
Puzzle 259 Not dividing any pandigital.




A000188 Prime Curios! Prime Puzzle
Wikipedia 188 Le nombre 188














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