Supported by my nephew and my niece Simar (16 years) and Simran (13) we solved an interesting maths problem, which might be unique as investigated by us on internet. We found the largest Prime Numbers which when shortened by deleting the last digit retains its primality. Example 37337999 is a number which when deleted by last number retains its primality, that is- 37337999, 3733799, 373379, 37337, 3733, 373, 37, 3.
Probed on internet. Seems, both the problem and the solution are unique.
We solved the problem to make some interesting discoveries.
First - the largest such number is 1979339339. All numbers
1979339339, 197933933, 19793393, 1979339, 197933, 19793, 1979, 197, 19, 1
The other largest such numbers starting with 2, 3, 5 & 7 are:
29399999, 37337999, 59393339, 7393933 (four)
The other very interesting observation is following - the number of possible cases (possible numbers ending with 1, 3, 7 & 9) turned out to be disproportionately large in case of those numbers that start with '1' vis a vis all other possible first digits - that is 2, 3, 5, & 7.
In all the five largest such numbers starting with 1, 2, 3, 5 & 7; 1, 2 & 5 appear only once, 7 appears 6 times, 3 appears 14 times and 9 is the most recurring 15 times.
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