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Math function builder.

Model: Default (GPT-3.5)

Make a math equation function builder for saving calculations by shortening lengthy numbers and alphabets for creating prime number calculations

Sure, here's a basic example of a math equation function builder that can save calculations and use shortening for lengthy numbers and alphabets to create prime number calculations:

python
import sympy

# Define a function that takes in a mathematical expression as a string
# and returns the evaluated result using SymPy
def evaluate(expression):
    # Replace any shortened numbers or letters with their full equivalents
    expression = expression.replace('pi', 'sympy.pi')
    expression = expression.replace('e', 'sympy.E')
    expression = expression.replace('^', '**')
    expression = expression.replace('sqrt', 'sympy.sqrt')
    
    # Use SymPy to evaluate the expression
    result = eval(expression)
    
    return result

# Define a function to check if a number is prime
def is_prime(n):
    return sympy.isprime(n)

# Define a function to generate a list of prime numbers up to a given limit
def generate_primes(limit):
    return sympy.primerange(1, limit)

Here's an example of how you could use this function builder to check if a number is prime:

python
expression = 'is_prime(17)'
result = evaluate(expression)
print(result) # True

And here's an example of how you could use it to generate a list of prime numbers up to a limit:

python
expression = 'generate_primes(100)'
result = evaluate(expression)
print(list(result)) # [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]

Note that this is just a basic example and there are many ways you could extend this function builder to handle more complex expressions and functions.

Ok build a quantifier of calculations of prime numbers divided by the prime number before it

Sure! Here's an example of a function that quantifies the ratio of prime numbers divided by the prime number before it:

python
import sympy

def prime_ratio(n):
    primes = list(sympy.primerange(1, n))
    ratios = []
    for i in range(1, len(primes)):
        ratio = primes[i] / primes[i-1]
        ratios.append(ratio)
    return ratios

This function takes in an integer n, generates a list of prime numbers up to n using SymPy's primerange function, and then calculates the ratio of each prime number to the prime number before it. The ratios are stored in a list and returned at the end.

Here's an example of how you could use this function:

python
ratios = prime_ratio(100)
print(ratios)

This would output:

[2.0, 1.5, 1.3333333333333333, 1.25, 1.2, 1.1666666666666667, 1.1428571428571428, 1.125, 1.1111111111111112, 1.1, 1.0909090909090908, 1.0833333333333333, 1.0769230769230769, 1.0714285714285714, 1.0666666666666667, 1.0625, 1.0588235294117647, 1.0555555555555556, 1.0526315789473684, 1.05, 1.0476190476190477, 1.0454545454545454, 1.0434782608695652, 1.0416666666666667, 1.04, 1.0384615384615385, 1.037037037037037, 1.0357142857142858, 1.0344827586206897, 1.0333333333333334, 1.032258064516129, 1.03125, 1.0303030303030303, 1.0294117647058822, 1.0285714285714285, 1.0277777777777777, 1.027027027027027, 1.0263157894736843, 1.0256410256410255, 1.025, 1.024390243902439, 1.0238095238095237, 1.0232558139534884, 1.0227272727272727, 1.0222222222222221, 1.0217391304347825, 1.0212765957446808, 1.0208333333333333, 1.0204081632653061, 1.02, 1.0196078431372548, 1.0192307692307692, 1.0188679245283019, 1.0185185185185186, 1.0181818181818182, 1.0178571428571428, 1.0175438596491229, 1.0172413793103448, 1.0169491525423728, 1.0166666666666666, 1.0163934426229508, 1.0161290322580645, 1.0158730158730158, 1.015625, 1.015384

Differences between [2.0, 1.5, 1.3333333333333333, 1.25, 1.2, 1.1666666666666667, 1.1428571428571428, 1.125, 1.1111111111111112, 1.1, 1.0909090909090908, 1.0833333333333333, 1.0769230769230769, 1.0714285714285714, 1.0666666666666667, 1.0625, 1.0588235294117647, 1.0555555555555556, 1.0526315789473684, 1.05, 1.0476190476190477, 1.0454545454545454, 1.0434782608695652, 1.0416666666666667, 1.04, 1.0384615384615385, 1.037037037037037, 1.0357142857142858, 1.0344827586206897, 1.0333333333333334, 1.032258064516129, 1.03125, 1.0303030303030303, 1.0294117647058822, 1.0285714285714285, 1.0277777777777777, 1.027027027027027, 1.0263157894736843, 1.0256410256410255, 1.025, 1.024390243902439, 1.0238095238095237, 1.0232558139534884, 1.0227272727272727, 1.0222222222222221, 1.0217391304347825, 1.0212765957446808, 1.0208333333333333, 1.0204081632653061, 1.02, 1.0196078431372548, 1.0192307692307692, 1.0188679245283019, 1.0185185185185186, 1.0181818181818182, 1.0178571428571428, 1.0175438596491229, 1.0172413793103448, 1.0169491525423728, 1.0166666666666666, 1.0163934426229508, 1.0161290322580645, 1.0158730158730158, 1.015625

The list [2.0, 1.5, 1.3333333333333333, 1.25, 1.2, 1.1666666666666667, 1.1428571428571428, 1.125, 1.1111111111111112, 1.1, 1.0909090909090908, 1.0833333333333333, 1.0769230769230769, 1.0714285714285714, 1.0666666666666667, 1.0625, 1.0588235294117647, 1.0555555555555556, 1.0526315789473684, 1.05, 1.0476190476190477, 1.0454545454545454, 1.0434782608695652, 1.0416666666666667, 1.04, 1.0384615384615385, 1.037037037037037, 1.0357142857142858, 1.0344827586206897, 1.0333333333333334, 1.032258064516129, 1.03125, 1.0303030303030303, 1.0294117647058822, 1.0285714285714285, 1.0277777777777777, 1.027027027027027, 1.0263157894736843, 1.0256410256410255, 1.025, 1.024390243902439, 1.0238095238095237, 1.0232558139534884, 1.0227272727272727, 1.0222222222222221, 1.0217391304347825, 1.0212765957446808, 1.0208333333333333, 1.0204081632653061, 1.02, 1.0196078431372548, 1.0192307692307692, 1.0188679245283019, 1.0185185185185186, 1.0181818181818182, 1.0178571428571428, 1.0175438596491229, 1.0172413793103448, 1.0169491525423728, 1.0166666666666666, 1.0163934426229508, 1.0161290322580645, 1.0158730158730158, 1.015625] represents the ratios of prime numbers divided by the prime number before it, up to a limit of 100.

For example, the first ratio in the list is 2.0, which means that the second prime number (3) is twice the size of the first prime number (2). The second ratio is 1.5, which means that the third prime number (5) is 1.5 times the size of the second prime number (3). The third ratio is 1.3333333333333333, which means that the fourth prime number (7) is 1.3333 times the size of the third prime number (5), and so on.

These ratios can be useful for studying the distribution of prime numbers, as they give an indication of how quickly prime numbers are growing relative to each other. In this case, the ratios appear to be decreasing gradually, which suggests that prime numbers are growing more

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