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Problem #374

Pandigital never prime
 Public ★(x14) 12/16/16 by Philippe_57721 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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