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[ January 13, 2013 ]
Gathering strictly pandigital probable primes (PRP's)
of the form ab^cdef +/- ghij
and various other formats you can come up with.

[ 2 | 4 | 4 ]

Here we will split up any strictly pandigital number (abcdefghij)
and form the general format ab^cdef+/-ghij into three parts [ 2 | 4 | 4 ]
and test the candidates for probable primeness. Of course
other partitionings/operations are allowed as well like
abc^def+/-ghij, ab!+cdefghij, etc.

First case takes place around the keynumber 10.

A pandigital is a 10-digit number where all the
digits from 0 to 9 appear once and only once.
The list I compiled is about the (probable)
primes around powers of 10 (complete).
I happened to find exactly 10 solutions (3-PRP!).

10^2435 + 9867
10^2569 + 4387
10^5863 + 2497
10^7325 + 6849
10^8459 + 2367

10^23856749
10^48629357
10^63547289
10^64357289
10^96538427

Underlined displacements means that the prp's are borderprp's.
The two highlighted prp's show a gem as only the digit 4 is moved.
All 10 exponents and 10 displacements are composite !

[ 2 | 5 | 3 ]

Range from 10^23456 –/+ 789 to 10^98765 –/+ 432
Both negative and positive displacements result alas in NO PRP solutions !

[ 2 | 1 | 7 ]

The smallest one with a positive 7-digit displacement is already prime !
10^2 + 3456789
Starting with base 10 and exponent 2 gives a total of 540 primes.
Quite abundant !
The largest by the way is 10^2 + 9876453.

[ 3 | 4 | 1 | 2 ]

Let me give you another format example of a pandigital PRP
expression. This is the place were you can submit your findings.
(please, avoid the digit 0 as a leading zero)

130 * 2456^7 + 89

[ 2 | 8 ]

In this section I searched some pandigital expressions
being equal to a palindrome !

10! + 48793625 = 52422425
10! + 49782635 = 53411435
10! + 68593427 = 72222227
10! + 69582437 = 73211237

10! - 53628794 = 49999994
10! - 73428596 = 69799796

12! + 67938045 = 546939645
12! + 70968345 = 549969945
12! + 87493065 = 566494665
12! + 90847365 = 569848965
12! + 93048675 = 572050275

13! - 52793084 = 6174224716

14! + 25639078 = 87203930278
14! + 93526078 = 87271817278

No solutions for 15!, 16! or 17!


[ E | N | D ]




A000182 Prime Curios! Prime Puzzle
Wikipedia 182 Le nombre 182














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Patrick De Geest - Belgium - Short Bio - Some Pictures
E-mail address : pdg@worldofnumbers.com