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Check the integers additive decomposition conjecture
Problem statement A conjecture (I rediscovered ?) related to Goldbach's one states that every integer above 2 can be written ...

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Check p² = 24k + 1, p > 3, the 'golden prime squares' equation
Historical context In december 2023, I / Nicolas Douillet was working on prime squares properties and I found* the formula : ...

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Fermat primes
Historical context The french mathematician Pierre de Fermat found the formula to find some prime numbers. He thought / co...

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Ulam primes first formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give the first 760 prime numbers ...

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Ulam primes second formula
Historical context The polish-american mathematician Stanislaw Ulam found the formula to give some prime numbers not given...

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Euler primes
Historical context The great swiss mathematician Leonhard Euler found the formula to give some prime numbers. Problem...

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Frequencies of prime gaps
Problem statement Given two positive integers n and , write a function which computes the frequency of the gap between two ...

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Find the first occurence of a given gap between two consecutive prime numbers
Problem statement Given a gap = p' - p between the two consecutive prime numbers p and p', find its first occurence, f. E...

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Prime numbers which are the difference of two consecutive cubes
Problem statement Given a positive integer n greater than 2, find the prime numbers less or equal to n and which are the diff...

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Partial Pressure of Water Vapor from Relative Humidity
Buck (1996, 1981) published the following constants for the saturation pressure of water*: 6.1121 (mb) The saturation pressur...

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Pressure for a given Above Sea Level Altitude
For altitudes up to the stratosphere (around 11 km above mean sea level), the air pressure can be estimated from: with where...

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Convert Volume Mixing Ratio to Density
The partial pressure of a constituent gas species of the atmosphere can be expressed in parts per million by volume. For exampl...

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Snow Accumulation and Structural Risks To Residential Properties
The density of snow depends on the amount of liquid water it contains: Dry Snow is about 50 kg/m^3 Wet Snow is about 200 kg/m^...

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Calculate Wind Chill Factor
The NWS Wind Chill Temperature (WCT) index formula for calculating the dangers from winter winds and freezing temperatures: Cal...

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Calculate the sphericity of a Raschig ring
Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of ...

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Molar Air Density from Temperature and Pressure
The molar density of air can be found from the Temperature and Pressure using the ideal gas law. where the Molar density STP ...

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Air Density from Temperature and Pressure
The density of air can be estimated from the product of molar mass and molar density: Write a function that finds the densi...

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Air Mass to Star for an Observer at Mean Sea Level
Air mass is a measure of how much atmosphere light from a source above the atmosphere (eg sun, planet, star) has to travel throu...

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Find Air Temperature from Cricket Stridulation Rate
Stridulation is the process that creates a cricket's “chirp” by rubbing their wings or legs. According to the Old Farmer's Alma...

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Predict Cricket Stridulation Rate from Air Temperature
Stridulation is the process that creates a cricket's “chirp” by rubbing their wings or legs. According to the Old Farmer's Alma...

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Find an optimal placement of coolers on a grid
In a certain chemical plant, 6 new pieces of cooling equipment (coolers) are to be installed in a vacant space. This vacant spac...

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Find an overlap in the cleaning schedule of two tank reactors
In a certain pharmaceutical production company, there are two tank reactors operating simultaneously and independent of each oth...

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Characterize fluid flow in a pipe as to laminar or turbulent
In fluid mechanics, characterizing the flow in a pipe is essential to predicting its behavior. The flow pattern can either be la...

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Assess the scatter of wind turbines in a field
The renewable energy industry is on the rise in many countries--- and one of the key players is wind energy. It is believed ...

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Design a tubesheet for shell-and-tube heat exchangers
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Convert a temperature reading from Celsius to an unknown scale
Two of the most famous temperature scales are the Celsius and the Fahrenheit scale. In reality, however, there are so many other...

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Count the number of folds needed to pack a large sheet
In a certain paper factory, large sheets of paper are being made every day. Before sending the sheets for shipment, they have to...

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Create a matrix map of increasing safety levels
The sole nuclear power plant at Grid City suddenly had a meltdown. Luckily, the plant was designed to be in full automation, so ...

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Weighted Convolution
Given two input vectors x = [x_1, x_2, ..., x_K] and y = [y_1, y_2, ..., y_K] of equal length, compute the weighted convolution ...

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Fletcher-Reeves Conjugate Gradient Method
Write a function to find the values of a design variable vector, _x_, that minimizes an unconstrained scalar objective function,...

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