# Category Archives: Prime Numbers

## Prime index of a palindromic hexagonal number

A hexagonal number is a polygonal number of the form       is a 19-digital prime index of the 39-digital palindromic hexagonal number:                                  … Continue reading

## Prime that is sum of consecutive triangular numbers with prime indices — Part 2

Prime that is sum of consecutive triangular numbers with prime indices — Part 1   Paul asks: If we consider the Index numbers 29 and 43, both prime and sum the consecutive triangular numbers with those prime indices the … Continue reading

## 13331 expressible as a sum of the squares of three consecutive odd triangular numbers

The odd triangular numbers are given by :   1, 3, 15, 21, 45, 55, 91, 105, 153, 171, 231, 253, 325, 351, 435, 465, 561, 595, 703, 741, 861, 903, 1035, 1081, 1225, 1275, 1431, 1485, 1653, … Continue reading

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## Num3er 1258723

A Pentagonal number is a polygonal number of the form     is a prime number.     is also prime index of a 13-digital palindromic pentagonal number                     … Continue reading

## Prime that is sum of consecutive triangular numbers with prime indices — Part 1

then,   is a prime number.   is the smallest prime that is sum of the first consecutive triangular numbers with prime indices.                             … Continue reading

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## Prime p; p^2 is the arithmetic mean of m^2 and n^2

Let     be a prime number and that there are 2 distinct positive integers     and   such that     is the arithmetic mean of     and   Prove that     is either … Continue reading

## Diophantine equation : y^2 – p = 2^n, where p is a prime number

The diophantine equation     where     is a prime number   < 100   The only solutions to the diophantine equation     with   y > 0   are given by     (n, y)   =   … Continue reading

## Four primes between the squares of two consecutive primes?

Claim:   There’s at least four primes between the squares of two consecutive primes,                    the first being > 3 Find a counterexample.                               … Continue reading