What is the general term formula for prime numbers What is the general term formula for prime number

Let's start by defining two concepts.

and a symbol.

x] represents the rounding down of x.

Concept 1If pn is the nth prime number, then pn x is equal to x divided by p1 to round down all prime numbers to pn, i.e.

x/p1]+[x/p2]+[x/p3]+.x/pn]

For example, if p3 = 5, then p3 x is equal to.

x/2]+[x/3]+[x/5]

Concept 2If pn is the nth prime number, then"pn is equal to the product of all combinations of prime numbers from p1 to pn (there must be at least 2 prime numbers in the combination of prime numbers).

For example, if p3=5, then"p3 is equal to the product of the combination of 2, 3, and 5, which is equal to.

And x"pn is equal to the rounding of the number obtained by dividing x by the above. It is also equal to:

x/(2*3)]

x/(2*5)]

x/(3*5)]

Now the recursive formula for prime numbers is given below.

2+pn#x-x"pn=x

As long as x is solved here, there may be many solutions, and the smallest solution is taken. Then x is equal to p(n+1).

This formula was deduced by me, and it is absolutely correct.

But this is just a recursive formula, and it's unlikely that you'll be able to move x to the side, (I can't prove it, but visually it's unlikely you'll be able to move x aside).So there is no general formula.

Here's an explanation of why there is no general term if x can't be moved to one side.

Suppose a sequence, the recursive formula can be written as a function.

a(n+1)=f(an)

Then the general formula is:

f(f(f(f(f...ax))) n fs

If f(an) this function cannot be represented by pure an.

Then the general term formula faces the same trouble.

So if I use a recursive formula, I can't move x aside. Then the formula for prime numbers may not exist.

There is no general formula for prime numbers, or the general formula for prime numbers has not yet been discovered, so many mathematicians spend a lot of energy on the distribution of prime numbers.

Let [x] be a Gaussian integer function.

The odd general formula that is not divisible by 3 is.

p(n)=2[n 2]+2n-1, in general, the odd general formula that is not divisible by the odd number p is.

p(n)=2[(n+p 2-3 2) (p-1)]+2n-1, and if the first term p is counted, then (p-1)[1 n] is added, so that the general formula for odd primes less than 25 is .

p(n)=2[n/2]+2n-1+2[1/n].

Continuing with the derivation, the odd primes less than 49 are .

p(n)=2[n/2]+2n-1+2[1/n]+(2[n/2+1/2]-2[n/2]+2)[n/10+1/10]

2[n/2+1/2]-2[n/2]+2+(2[n/2+1]+2[n/2])[n/10+2/10])[n/10-1/10].

or p(n)=2[(n+[n 8-3 8]+[n 8-1 8]) 2] +2(n+[n 8-3 8]+[n 8-1 8])-1+4[2 n]-4[1 n].

However, if this continues, only a limited number of items can be listed.

Does there exist such a thing as a universal term for prime numbers?

<>< 2, 3, 5, 7, 11, 13, 17, etc.

Prime number. There is a series of prime numbers, but so far no number scientist has found a general formula that can represent the number series hall town.

Prime numbers are more than juxtaposed.

Let's start by defining two concepts.

and a symbol.

x] represents the rounding down of x.

Concept 1If pn is the nth prime number.

Then pn x is equal to x divided by p1 to pn and all prime numbers are rounded down, i.e.,

x/p1]+[x/p2]+[x/p3]+.x pn], for example, if p3=5, then p3 x is equal to.

x/2]+[x/3]+[x/5]

Concept 2If pn is the nth prime number, then"pn is equal to the product of all combinations of prime numbers from p1 to pn (there must be at least 2 prime numbers in the combination of prime numbers).

For example, if p3=5, then"p3 is equal to.

The product of the combination of 2, 3, and 5 is equal to.

And x"pn is equal to the rounding of the number obtained by dividing x by the above. It is also equal to:

x/(2*3)]

x/(2*5)]

x/(3*5)]

Now the recursive formula for prime numbers.

As follows. 2+pn#x-x"pn=x

As long as x is solved here, there may be many solutions, and the smallest solution is taken. Then the formula x is equal to p(n+1) in the early spring is what I deduced, and it is absolutely correct.

But this is just a recursive formula, and it's unlikely that you'll be able to move x to the side, (I can't prove it, but intuitively you're unlikely to move x aside).So the general term formula.

It doesn't exist.

Here's an explanation of why there is no general term if x can't be moved to one side.

Suppose a sequence, the recursive formula can be written as a function.

a(n+1)=f(an)

Then the general formula is:

f(f(f(f(f...ax)))

n f if f(an) cannot be represented by pure an.

Then the general term formula faces the same trouble.

So if I use a recursive formula, I can't move x aside. Then the formula for prime numbers may not exist.

Let [x] be a Gaussian integer function, an odd general that is not divisible by 3.

p(n)=2[n 2]+2n-1, in general, the odd general formula that is not divisible by the odd number p is.

p(n)=2[(n+p 2-3 difference round silver2) (p-1)]+2n-1, into the first term p, then add (p-1)[1 n], thus, the general formula for odd primes less than 25 is.

p(n)=2[n/2]+2n-1+2[1/n].

Continuing with the derivation, the odd primes less than 49 are .

p(n)=2[n 2]+2n-1+2[1 n]+(2[n 2+1 2]-2[n 2]+2)[n 10+1 virtual feast 10].

2[n cavity celery 2+1 2]-2[n 2]+2+(2[n 2+1]+2[n 2])[n 10+2 10])[n 10-1 10].

or p(n)=2[(n+[n 8-3 8]+[n 8-1 8]) 2].

2(n+[n/8-3/8]+[n/8-1/8])-1+4[2/n]-4[1/n].

However, if this continues, only a limited number of items can be listed.

This rule is simple and bright, but it is easy to find a pattern.

As you said, the latter is equal to the previous plus 、...

In this case, the general term = the first term + (0 + 1 + 2 + .n-1) an=1+(0+1+.n-1))

1+(n-1)n/2

n -n+2) 2, n belongs to the bond segment n+