Enigma 1075: No factors
12 February 2018
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From New Scientist #2231, 25th March 2000 [link]
I have found a five-digit number such that it is impossible to factorise the numbers formed by its first digit or last digit or first two digits or last two digits or first three digits or last three digits or first four digits or last four digits or all five digits. In other words all those numbers are prime except that either or both of the single digit numbers may be unity.
Identify the five-digit number.