Given two integers **X** and **Y**, the task is to perform the following operations:

- Find all prime numbers in the range
**[X, Y]**. - Generate all numbers possible by combining every pair of primes in the given range.
- Find the prime numbers among all the possible numbers generated above. Calculate the count of primes among them, say
**N**. - Print the N
^{th}term of a Fibonacci Series formed by having the smallest and largest primes from the above list as the first two terms of the series.

**Examples:**

Input:X = 2 Y = 40

Output:34

Explanation:

All primes in the range [X, Y] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37]

All possible numbers generated by concatenating each pair of prime = [23, 25, 27, 211, 213, 217, 219, 223, 229, 231, 32, 35, 37, 311, 313, 319, 323, 329, 331, 337, 52, 53, 57, 511, 513, 517, 519, 523, 529, 531, 537, 72, 73, 75, 711, 713, 717, 719, 723, 729, 731, 737, 112, 113, 115, 117, 1113, 1117, 1119, 1123, 1129, 1131, 1137, 132, 133, 135, 137, 1311, 1317, 1319, 1323, 1329, 1331, 1337, 172, 173, 175, 177, 1711, 1713, 1719, 1723, 1729, 1731, 1737, 192, 193, 195, 197, 1911, 1913, 1917, 1923, 1929, 1931, 1937, 232, 233, 235, 237, 2311, 2313, 2317, 2319, 2329, 2331, 2337, 292, 293, 295, 297, 2911, 2913, 2917, 2919, 2923, 2931, 2937, 312, 315, 317, 3111, 3113, 3117, 3119, 3123, 3129, 3137, 372, 373, 375, 377, 3711, 3713, 3717, 3719, 3723, 3729, 3731]All primes among the generated numbers=[193, 3137, 197, 2311, 3719, 73, 137, 331, 523, 1931, 719, 337, 211, 23, 1117, 223, 1123, 229, 37, 293, 2917, 1319, 1129, 233, 173, 3119, 113, 53, 373, 311, 313, 1913, 1723, 317]

Count of the primes = 34

Smallest Prime = 23

Largest Prime = 3719

Therefore, the 34th term of the Fibonacci series having 23 and 3719 as the first two terms, is 13158006689.

Input:X = 1, Y = 10

Output:1053

**Approach: **

Follow the steps below to solve the problem:

- Generate all possible primes using
**Sieve of Eratothenes**. - Traverse the range
**[X, Y]**and generate all primes in the range with the help of**primes[]**array generated in the step above. - Traverse the list of primes and generate all possible pairs from the list.
- For each pair, concatenate the two primes and check if their concatenation is a prime or not.
- Find the
**maximum**and**minimum**of all such primes and count all such primes obtained. - Finally, print the
**count**^{th}of a Fibonacci series having**minimum**and**maximum**obtained in the above step as the first two terms of the series.

Below is the implementation of the above approach:

## Python

`# Python Program to implement ` `# the above approach ` ` ` `# Stores at each index if it's a ` `# prime or not ` `prime ` `=` `[` `True` `for` `i ` `in` `range` `(` `100001` `)] ` ` ` `# Sieve of Eratosthenes to ` `# generate all possible primes ` `def` `SieveOfEratosthenes(): ` ` ` ` ` `p ` `=` `2` ` ` `while` `(p ` `*` `p <` `=` `100000` `): ` ` ` ` ` `# If p is a prime ` ` ` `if` `(prime[p] ` `=` `=` `True` `): ` ` ` ` ` `# Set all multiples of p as non-prime ` ` ` `for` `i ` `in` `range` `(p ` `*` `p, ` `100001` `, p): ` ` ` `prime[i] ` `=` `False` ` ` ` ` `p ` `+` `=` `1` ` ` `# Function to generate the ` `# required Fibonacci Series ` `def` `fibonacciOfPrime(n1, n2): ` ` ` ` ` `SieveOfEratosthenes() ` ` ` ` ` `# Stores all primes between ` ` ` `# n1 and n2 ` ` ` `initial ` `=` `[] ` ` ` ` ` `# Generate all primes between ` ` ` `# n1 and n2 ` ` ` `for` `i ` `in` `range` `(n1, n2): ` ` ` `if` `prime[i]: ` ` ` `initial.append(i) ` ` ` ` ` `# Stores all concatenations ` ` ` `# of each pair of primes ` ` ` `now ` `=` `[] ` ` ` ` ` `# Generate all concatenations ` ` ` `# of each pair of primes ` ` ` `for` `a ` `in` `initial: ` ` ` `for` `b ` `in` `initial: ` ` ` `if` `a !` `=` `b: ` ` ` `c ` `=` `str` `(a) ` `+` `str` `(b) ` ` ` `now.append(` `int` `(c)) ` ` ` ` ` `# Stores the primes out of the ` ` ` `# numbers generated above ` ` ` `current ` `=` `[] ` ` ` ` ` `for` `x ` `in` `now: ` ` ` `if` `prime[x]: ` ` ` `current.append(x) ` ` ` ` ` `# Store the unique primes ` ` ` `current ` `=` `set` `(current) ` ` ` ` ` `# Find the minimum ` ` ` `first ` `=` `min` `(current) ` ` ` ` ` `# Find the minimum ` ` ` `second ` `=` `max` `(current) ` ` ` ` ` `# Find N ` ` ` `count ` `=` `len` `(current) ` `-` `1` ` ` `curr ` `=` `1` ` ` ` ` `while` `curr < count: ` ` ` `c ` `=` `first ` `+` `second ` ` ` `first ` `=` `second ` ` ` `second ` `=` `c ` ` ` `curr ` `+` `=` `1` ` ` ` ` `# Print the N-th term ` ` ` `# of the Fibonacci Series ` ` ` `print` `(c) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` ` ` `x ` `=` `2` ` ` `y ` `=` `40` ` ` `fibonacciOfPrime(x, y) ` |

*chevron_right*

*filter_none*

**Output:**

13158006689

**Time Complexity:** O(N^{2} + log(log(maxm))), where it takes O(N^{2}) to generate all pairs and O(1) to check if a number is prime or not and maxm is the size of prime[]

**Auxiliary Space:** O(maxm)

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