## 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.

math grad - Interest: Number theory
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### 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