Haskell is a programming language that changes the regular imperative way that we program.

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For the equation.

We use the solutions of the equation Pell.

Then the solution can write.

And again.

All the numbers can have any sign.

]]>https://facebook.com/ShuugakuHitoKaraKanjiNiNarau/

This is the first image which I uploaded there:

The Kanji for 1, 2, and 3 are similar to their Roman numeral (I, II, and III) rotated 90 degrees (一, 二 and 三).]]>

I think they still use the Elliptic curves ECF or Quadratic Sieves.

Take a look here:

https://www.alpertron.com.ar/ECM.HTM

]]>Do not worry about it, it is okay. It is enough that you have it. Post if you get stuck on one or find one interesting.

I will not get stuck since i have the solutions book(yes a solutions book is also available there.....). Yeah i will send you the questions which i find difficult and interesting.

]]>https://brilliant.org/wiki/converse-of-intermediate-value-theorem/

]]>A=2x3x5x7x11x13x17........ up to

m=Any multiple

A-pm= A number factorable by a factor of p

if p has one.To get A-pm, go through the primes, subtracting p as many times as you like.

Example:

p=129

A=2x3x5x7x11

2x3x5x7=210 210-129=81

81x11=891 891-(129x6)=117

A-129m=117

117 will have a factor the same as p if it has any.

117/129=39/43 129 is NOT prime (Common denominator =3)

In this way we can find out if p is composite without ever having to use a number

. Might be useful for computers.]]>Example:

p=130

Rd. Up to nearest prime= 13

Next prime after that = 17

17-1=16

Largest prime gap <130 = 16 (Correct)

This works because the greatest number of composites between two primes occurs when factors are not combined. So what could have been two composites is actually just one, like 15=3x5. To create the greatest possible number of composites I start at 2 not 0. 0 has an infinite number of prime factors, and so the greatest gap between the next repeat will occur after 0. Starting with the smallest composite which is NOT combined factors, I move up. Deleting all numbers factorable by primes less than the square root. The first time I attain TWO primes is when I reach the second prime after the square root. So this -1 is the gap required to create two non-composites with greatest possible occurrence of composites.

Largest prime gap <p =

Rd. Up to second nearest prime -1.]]>