Cuban Prime

Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. For examples, 2, 3, 5, 7, 11, 13, etc. There are many types of prime number based on different properties. One such types of prime is called Cuban Prime. They are named after the Cuban mathematician Claudio Gil Pérez.

Cuban primes are generated using particular mathematical formulas involving cube numbers. These follows one of the two mathematical equation:

First Kind of Cuban primes: These primes can be expressed in the form of:

Where x = y + 1 and p is a prime number. In simpler terms, they come from the difference of cubes of two consecutive integers.

Examples:

• When x = 2 and y = 1, the equation becomes p = 2² + 2(1) + 1² = 4 + 2 + 1 = 7, so 7 is a Cuban prime.
• When x = 3 and y = 2, the equation becomes p = 3² + 3(2) + 2² = 9 + 6 + 4= 19, so 19 is also a Cuban prime.

Second Kind of Cuban primes: These are primes that can be expressed in the form of:

Where n is a positive integer, and p is a prime number.

Examples:

• When n = 1, the equation becomes, so 37 is a Cuban prime of the second kind.
• When n = 2, , so 127 is a cube prime of second kind.

Both forms produces different types of Cuban prime.

Examples of First Form of Cuban Primes

Some examples of first kind Cuban primes are:

7, 19, 37, 61, 127, 271, 331, 397, 491, 547, 631, 919, 1657, 1801, 1951, 2269, 2437, 2791, 3169, . . .

Examples of Second Form of Cuban Primes

Some examples of second kind Cuban primes are:

13, 109, 193, 433, 769, 1201, 1453, 2029, 3469, 3889, 4801, 10093, 12289, 13873, 18253, 20173, 21169, 22189, 28813, 37633, . . .

Conclusion

In conclusion, Cuban primes are a unique and fascinating category of prime numbers, derived from specific algebraic formulas. They come in two forms first and second, both were discussed in the article in detail.

Read More,

• Composite Numbers
• Cullen Primes
• Repunit Primes