perplexus.info :: Numbers : Semiprimes and Emirps

Semiprimes and Emirps (Posted on 2023-01-14)

Determine the total number of semiprimes below 2023, that are immediately followed by an emirp.

For example, 22 is a semiprime which is immediately followed by 23. But 23 is NOT an emirp, since 32 is composite.

List all valid pairs in conformity with the provisions of the problem.

*** Computer program/ excel solver aided methods are welcome, but a semi-analytic methodology is preferred.

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

Without including palindromes, there are precisely 11 valid semiprimes. However, there are precisely 15 valid semiprimes when we include palindromes.
For an explanation, refer to the computer program assisted solution submitted by Charlie, without palindromes, in this location and a list of such semiprimes, with palindromes, in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): semi-analytic solution	Steven Lord	2023-01-14 11:16:03
re: semi-analytic solution	Charlie	2023-01-14 11:05:15
computer solution	Charlie	2023-01-14 11:01:12
semi-analytic solution	Steven Lord	2023-01-14 10:54:39
Computer solution	Larry	2023-01-14 10:09:25

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