Problem #374

Pandigital never prime
Public 12/16/16 5xp Programming 48.3%

Consider the number 100020
If you change one of its digits, you never get a prime number:

100020= $ {2}^{2}\times 3\times 5\times 1667 $
200020= $ {2}^{2}\times 5\times 73\times 137 $
300020= $ {2}^{2}\times 5\times 7\times 2143 $
400020= $ {2}^{2}\times 3\times 5\times 59\times 113 $
500020= $ {2}^{2}\times 5\times 23\times 1087 $
600020= $ {2}^{2}\times 5\times 19\times 1579 $
700020= $ {2}^{2}\times {3}^{2}\times 5\times 3889 $
800020= $ {2}^{2}\times 5\times 13\times 17\times 181 $
900020= $ {2}^{2}\times 5\times 11\times 4091 $

100020= $ {2}^{2}\times 3\times 5\times 1667 $
110020= $ {2}^{2}\times 5\times 5501 $
120020= $ {2}^{2}\times 5\times 17\times 353 $
130020= $ {2}^{2}\times 3\times 5\times 11\times 197 $
140020= $ {2}^{2}\times 5\times 7001 $
150020= $ {2}^{2}\times 5\times 13\times 577 $
160020= $ {2}^{2}\times {3}^{2}\times 5\times 7\times 127 $
170020= $ {2}^{2}\times 5\times 8501 $
180020= $ {2}^{2}\times 5\times 9001 $
190020= $ {2}^{2}\times 3\times 5\times 3167 $

100020= $ {2}^{2}\times 3\times 5\times 1667 $
101020= $ {2}^{2}\times 5\times 5051 $
102020= $ {2}^{2}\times 5\times 5101 $
103020= $ {2}^{2}\times 3\times 5\times 17\times 101 $
104020= $ {2}^{2}\times 5\times 7\times 743 $
105020= $ {2}^{2}\times 5\times 59\times 89 $
106020= $ {2}^{2}\times {3}^{2}\times 5\times 19\times 31 $
107020= $ {2}^{2}\times 5\times 5351 $
108020= $ {2}^{2}\times 5\times 11\times 491 $
109020= $ {2}^{2}\times 3\times 5\times 23\times 79 $

100020= $ {2}^{2}\times 3\times 5\times 1667 $
100120= $ {2}^{3}\times 5\times 2503 $
100220= $ {2}^{2}\times 5\times 5011 $
100320= $ {2}^{5}\times 3\times 5\times 11\times 19 $
100420= $ {2}^{2}\times 5\times 5021 $
100520= $ {2}^{3}\times 5\times 7\times 359 $
100620= $ {2}^{2}\times {3}^{2}\times 5\times 13\times 43 $
100720= $ {2}^{4}\times 5\times 1259 $
100820= $ {2}^{2}\times 5\times {71}^{2} $
100920= $ {2}^{3}\times 3\times 5\times {29}^{2} $

100000= $ {2}^{5}\times {5}^{5} $
100010= $ 2\times 5\times 73\times 137 $
100020= $ {2}^{2}\times 3\times 5\times 1667 $
100030= $ 2\times 5\times 7\times 1429 $
100040= $ {2}^{3}\times 5\times 41\times 61 $
100050= $ 2\times 3\times {5}^{2}\times 23\times 29 $
100060= $ {2}^{2}\times 5\times 5003 $
100070= $ 2\times 5\times 10007 $
100080= $ {2}^{4}\times {3}^{2}\times 5\times 139 $
100090= $ 2\times 5\times 10009 $

100020= $ {2}^{2}\times 3\times 5\times 1667 $
100021= $ 29\times 3449 $
100022= $ 2\times 13\times 3847 $
100023= $ 3\times 7\times 11\times 433 $
100024= $ {2}^{3}\times 12503 $
100025= $ {5}^{2}\times 4001 $
100026= $ 2\times {3}^{2}\times 5557 $
100027= $ 23\times 4349 $
100028= $ {2}^{2}\times 17\times 1471 $
100029= $ 3\times 33343 $


What is the smallest pandigital number (in base 10) with that property? (*)
(*) All the numbers you get when changing one digit must be pandigital too.


[My timing: < 1 sec]



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