Special triplets (a,b,c): palindrome, square, and prime

 
 

Here are three different triplets of consecutive integers such that

>>   the first term of each triplet is a palindrome,
>>   the second a square,
>>   the third a prime.

 

(3,   4,   5)

(99,   100,   101)

(575,   576,   577)

 

Are there any other triplets satisfying those conditions?

 

Pipo found:

518286020682815   is a palindrome number
518286020682816 \; = \; 22765896^2
518286020682817   is a prime number.

995570353075599   is a palindrome number
995570353075600 \; = \; 31552660^2
995570353075601   is a prime number.

 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Prime Numbers and tagged , . Bookmark the permalink.

3 Responses to Special triplets (a,b,c): palindrome, square, and prime

  1. pipo says:

    Found two bigger ones:
    (518286020682815, 518286020682816, 518286020682817) where 518286020682816=22765896^2
    (995570353075599, 995570353075600, 995570353075601) where
    995570353075600 =31552660^2

    pipo

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