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A while ago, I had a look at the prime factorization of 27000:

27000 = 2³ × 3³ × 5³

There are two special things about that:

• consecutive-prime: The primes are consecutive: 2 is the 1st prime, 3 is the 2nd prime, 5 is the 3rd prime.
• constant-exponent: The exponent is the same for every prime (always 3)

Mathematically expressed:

An integer x is a consecutive-prime/constant-exponent number if there exist strictly positive integers n, k, m such that x = p_n^m × p_n+1^m × ... × p_n+k^m, where p_j is the j-th prime

Your task is to test if a positive integer fulfills these conditions.

Input:

A positive integer > 1, in any reasonable form.

Output:

One of two values, at least one of which has to be constant, indicating whether the input is a consecutive-prime/constant-exponent number.

Edge cases:

• primes are truthy, as the factorization for prime p is p¹
• other numbers that can be written as p^m where p is a prime are also truthy.

Rules:

• Standard loopholes apply.
• No worries about integer overflow, but numbers up to 255 must work.
• Shortest code in bytes wins.

Test cases:

Truthy:

2
3
4
5
6
7
8
9
11
13
15
27000
456533

Falsy:

10
12
14
72
10000000

Here is a python script generating some test cases.

###The fact that I accepted an answer does not mean that the challenge is over; the winner can still change!

A while ago, I had a look at the prime factorization of 27000:

27000 = 2³ × 3³ × 5³

There are two special things about that:

• consecutive-prime: The primes are consecutive: 2 is the 1st prime, 3 is the 2nd prime, 5 is the 3rd prime.
• constant-exponent: The exponent is the same for every prime (always 3)

Mathematically expressed:

An integer x is a consecutive-prime/constant-exponent number if there exist strictly positive integers n, k, m such that x = p_n^m × p_n+1^m × ... × p_n+k^m, where p_j is the j-th prime

Your task is to test if a positive integer fulfills these conditions.

Input:

A positive integer > 1, in any reasonable form.

Output:

One of two values, at least one of which has to be constant, indicating whether the input is a consecutive-prime/constant-exponent number.

Edge cases:

• primes are truthy, as the factorization for prime p is p¹
• other numbers that can be written as p^m where p is a prime are also truthy.

Rules:

• Standard loopholes apply.
• No worries about integer overflow, but numbers up to 255 must work.
• Shortest code in bytes wins.

Test cases:

Truthy:

2
3
4
5
6
7
8
9
11
13
15
27000
456533

Falsy:

10
12
14
72
10000000

Here is a python script generating some test cases.

The fact that I accepted an answer does not mean that the challenge is over; the winner can still change!

A while ago, I had a look at the prime factorization of 27000:

27000 = 2³ × 3³ × 5³

There are two special things about that:

• consecutive-prime: The primes are consecutive: 2 is the 1st prime, 3 is the 2nd prime, 5 is the 3rd prime.
• constant-exponent: The exponent is the same for every prime (always 3)

Mathematically expressed:

An integer x is a consecutive-prime/constant-exponent number if there exist strictly positive integers n, k, m such that x = p_n^m × p_n+1^m × ... × p_n+k^m, where p_j is the j-th prime

Your task is to test if a positive integer fulfills these conditions.

Input:

A positive integer > 1, in any reasonable form.

Output:

One of two values, at least one of which has to be constant, indicating whether the input is a consecutive-prime/constant-exponent number.

Edge cases:

• primes are truthy, as the factorization for prime p is p¹
• other numbers that can be written as p^m where p is a prime are also truthy.

Rules:

• Standard loopholes apply.
• No worries about integer overflow, but numbers up to 255 must work.
• Shortest code in bytes wins.

Test cases:

Truthy:

2
3
4
5
6
7
8
9
11
13
15
27000
456533

Falsy:

10
12
14
72
10000000

Here is a python script generating some test cases.

A while ago, I had a look at the prime factorization of 27000:

27000 = 2³ × 3³ × 5³

There are two special things about that:

• consecutive-prime: The primes are consecutive: 2 is the 1st prime, 3 is the 2nd prime, 5 is the 3rd prime.
• constant-exponent: The exponent is the same for every prime (always 3)

Mathematically expressed:

An integer x is a consecutive-prime/constant-exponent number if there exist strictly positive integers n, k, m such that x = p_n^m × p_n+1^m × ... × p_n+k^m, where p_j is the j-th prime

Your task is to test if a positive integer fulfills these conditions.

Input:

A positive integer > 1, in any reasonable form.

Output:

One of two values, at least one of which has to be constant, indicating whether the input is a consecutive-prime/constant-exponent number.

Edge cases:

• primes are truthy, as the factorization for prime p is p¹
• other numbers that can be written as p^m where p is a prime are also truthy.

Rules:

• Standard loopholes apply.
• No worries about integer overflow, but numbers up to 255 must work.
• Shortest code in bytes wins.

Test cases:

Truthy:

2
3
4
5
6
7
8
9
11
13
15
27000
456533

Falsy:

10
12
14
72
10000000

Here is a python script generating some test cases.

###The fact that I accepted an answer does not mean that the challenge is over; the winner can still change!