Prime Heaven (Problem 1, Version 2)

Find a double-digit prime $xy$ that when:

Its digits are squared, added together and square rooted, it produces a prime that is simultaneously a Fibonacci number, a Bell number, a Catalan number, a Fermat number and a Fermat prime

Its digits are added, it produces a prime that is simultaneously a Lucas number

Its digits are multiplied together and the digits of the resulting number are added together, it produces a prime that is simultaneously a Fibonacci number, a Lucas number, a Fermat number and a Fermat prime

Its digits are divided like this: $\frac{x}{y}$ , the numbers after the decimal point are all prime and are simultaneously a Fibonacci number, a Lucas number, a Fermat number and a Fermat prime

Its digits are divided like this $\frac{y}{x}$ , the numbers after the decimal point are prime - the first digit after the decimal point is a Lucas number and the second number after the decimal point is a Bell number, Fibonacci number, a Catalan number, a Fermat number and a Fermat prime

Its digits are subtracted like this: $x - y$ , it simultaneously equals a Bell number, a Lucas number, a Catalan number and a Fibonacci number

Its digits are subtracted like this: $y - x$ , it simultaneously equals a negative Bell number, a negative Lucas number, a negative Catalan number and a negative Fibonacci number

Its digits are squared and added, the resulting number's digits are prime - the first digit is simultaneously a Lucas number and a Catalan number, the second digit is simultaneously a Fibonacci number, a Bell number, a Catalan number, a Fermat number and a Fermat prime

Its digits are squared and added and the resulting number's digits are added, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the fourth power and added together, the digits of the resulting number is prime - the first two digits are simultaneously a Fibonacci number and a Lucas number and the last digit is simultaneously a Lucas number

Its digits are raised to the fourth power and added together and the digits of the resulting number are added, it produces a prime that is simultaneously a Fibonacci number

Its digits are raised to the fifth power and the resulting number's digits are added together, it produces a prime that is simultaneously a Bell number, a Lucas number, a Catalan number and a Fibonacci number raised to the fourth power

Its digits are raised to the fifth power and the resulting number's digits are added together and the next resulting number's digits are added together, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the sixth power and the resulting number's digits are added together, it produces a prime

Its digits are squared and added together and the resulting number's digits are added, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the fourth power and the resulting number's digits are added, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the seventh power and the resulting number's digits are added, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the eighth power and the resulting number's digits are added, it produces a prime that is simultaneously a Bell number, a Catalan number, a Fibonacci number, a Fermat number and a Fermat prime squared

Its digits are raised to the eighth power and the resulting number's digits are added and the next resulting number's digits is added together, it produces a prime that is simultaneously a Lucas number

Its digits are raised to the eleventh power and the resulting number's digits are added together, it produces a prime that is simultaneously a Bell number, a Catalan number, a Fibonacci number, a Fermat number and a Fermat prime squared

Its digits are raised to the twelfth power and the resulting number's digits are added together, it produces a prime which its digits are also prime - the first digit is simultaneously a Bell number, a Catalan number, a Fibonacci number, a Fermat number and a Fermat prime - the second digit is simultaneously a Lucas number

The first digit is square rooted and added with the second digit, it produces a prime that is simultaneously a Fibonacci number, a Bell number, a Catalan number, a Fermat number and a Fermat prime

$x$ is simultaneously a prime that is simultaneously a Bell number, a Lucas number, a Catalan number and a Fibonacci number squared

$x$ is simultaneously a Lucas number

$x$ can be split into $3$ different sums - the first sum involves two numbers - the first number involved is simultaneously a Fibonacci number and the second number involved is a Lucas number, the second sum involves two numbers that are simultaneously a Bell number, a Lucas number, a Catalan number, a Fibonacci number, a Fermat number and a Fermat prime and the third sum involves two numbers - the first number involved is simultaneously a Bell number, a Lucas number, a Catalan number and a Fibonacci number and the second number involved is simultaneously a Fibonacci number and a Lucas number

$y$ is simultaneously a Fibonacci number, a Lucas number, a Fermat number and a Fermat prime

$y$ can be split into $2$ different sums - the first sum involves two numbers that are simultaneously a Bell number, a Lucas number, a Catalan number and a Fibonacci number, the second sum involves two numbers that are simultaneously a Fibonacci number, a Lucas number, a Fermat number and a Fermat prime