Each radical ideal in the ring of algebraic integers is a finite intersection of prime ideals

Does every radical ideal in the ring of algebraic integers (that is, the integral closure of $ mathbb {Z} $ considered a subgroup of $ mathbb {C} $ via the unique homomorphism of plain rings $ mathbb {Z} rightarrow mathbb {C} $) a finite intersection of prime ideals?

Problem with prime numbers, Python 3

I am a beginner, I can not solve the following problem, find all prime numbers in a set of 1 to 1000.

I want the code to store the numbers in a result list.

here is my attempt:

list = []
result = []
cont = 0

for i in the range (1, 1001):
list.append (i)
for j in the list:
for i in the range (1, 1001):
if j% i == 0:
cont + = 1
if cont == 2:
result.append (j)
cont = 0
print (result)

Amazon Prime Customer Service – SEO Help (General Discussion)


Many entrepreneurs complain that it is difficult to operate a store. Many chefs complain that operators are not doing their job well. Many operators feel wronged and obviously work but can not find ways to improve their performance. All sorts of complaints can be summed up in one sentence: The operation does not succeed.

Why the operation does not work?

It seems that everyone is working in the right direction, but why does not the operation work? There are only two reasons: neither obey nor execute.

The operation is not as difficult as you imagine. When you see someone around you doing very well, you really approve it. But you can think that his feat is only luck! However, your own fortune never comes, so you are always depressed.

If you read more skill articles, you will find that it is nothing more. Many of them repeat a topic again and again. It is better to practice them one by one than to learn more skills. Operation is not difficult, so that you do not have good. The first reason is that you are not obedient.

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How to operate the operation?

How do you understand the reason? For example, many salespeople read many articles on business skills daily and even every employee in the company reads articles on a daily basis.

When writing an article and sharing an experience or point of view, most participants want to share what they think is most important. But the reader may not be very attentive to reading. Even if someone reads it, he will feel "seems useful" or "just blah" instead of trying to think like whoever shares it: what is the purpose of this sharing? What kind of real experience behind the text? What does it mean to transmit beyond words?

If you can think a little more, you will get a different result if you read a tip. But if you keep a self-complacent attitude and navigate like a dragonfly, its benefits are also limited.

In addition, "Obedient" also requires a very important condition: you may need to change your mind. Ordinary people are used to "understand first and then accept". But with that mind, what you accept is often what you already know. Even if you accept it, it does not mean that you have progressed. To achieve the "obedient" goal, in order to progress better, you may have to "accept first, then understand". In this last mode of thinking, it is only a change of position. The position has changed and progress will soon be made.

"Obedient" means a step forward. But at this stage, progress is only internal and has not been demonstrated. If you want to transform our internal growth into improved operational performance, you must "run".

To tell the truth, the performance is the most boring. You must not only perform simple steps, but also repeat them and even repeat them a hundred times. But it is the repetition of these simple steps that will allow you to acquire a very skillful ability.

By "obedient", you capture the vision and method of people with more experience than you. By "execution", you internalize the knowledge in your own ways of functioning. When you turn this new knowledge into abilities, you will discover how ignorant you were before.

At that time, your performance will increase unconsciously. Then you will oppose seeing those honest sellers who struggle and are unable to relieve themselves.

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Is there an analogy with twin prime numbers in rational integers among Gaussian and Eisenstein integers?

The twin prime numbers, like (29, 31) and (137, 139) are interesting to study. I have explored the parallels of Gaussian and Eisenstein integers with rational integers. For example, they have prime numbers and composites in common. But are there "twin primes"? There may not be any direct analogy, since the relations> and <are ambiguous in the whole numbers of Gauss and Eisenstein – unless you speak of the norm.

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beginner – search the prime factors of the number

I have tried to create a small program to find the prime factors of the number and their decomposition. I would love to receive some tips to improve my code or modify it, especially since I'm still noob. Thank you !

def prime_factors (x):
divisors = []
    for y in the beach (1, x + 1):
if x% y == 0: divisors + = [y]       "" "it creates a parameter divider list" ""
divisors = sorted (divisors)
divisorsList = prime_number (divisors)
label = power (divisorsList, x)
return label

def prime_number (lists):
"" "returns a list of prime numbers" ""
target = []
    for x in the lists:
account = 0
for there in the lists:
if x% y == 0: number + = 1 "" "gets the number of number divisors from the past list: they must be 2" ""
if account == 2: target + = [x]     "" "If so, add a prime number to the" "list
return target

def power (lists, x):
"" "returns the list of prime numbers and their decomposition into dictionary" ""
label = {}
for t in the lists:
account = 0
while x% t == 0:
head = x / t
x = head
account + = 1
return label

Huwei Y6 Prime Secure File Not Found!

My phone is Huwei Y6 Prime.Today, I wanted to grab it.But the file was not found.Create it a new one.J I created a new one.But I am still unable to look at my photos and pictures those that I have kept in a safe..But it stays in the optional files SD card .. But I can not open it.There are there a way to recover my photos😫

Motherboard – PRIME X299-DELUXE II Thunderbolt Display with RTX 2080

I just built a new PC in the hope of using it with my Apple Thunderbolt screen, but no luck at the moment. Sometimes it works, then turns it off intermittently, at other times it prevents startup. Here are the specifications of the construction:

Operating system: Windows 10
MoBo: Asus Prime X299 Deluxe II
GPU: RTX 2080
CPU: i9-9900x

I have the GPU connected to DisplayPort IN and the screen connected to the Thunderbolt 3 jack. Based on how it behaves with a good rendering, then cutting in circles would suppose a bandwidth / problem speed.

I've built a PC almost identical 6 months ago (this one is for my employee), but with the previous generation Asus Prime X299 Deluxe and a 1080i GTX that works perfectly with my Apple Thunderbolt display.

Has anyone managed to use a Thunderbolt screen on the new Prime X299 Deluxe II model? All the indicators on the calculation would be amazing. Hit a brick wall …

prime numbers – code for creating a sequence

I would like the Mathematica code to create this sequence to be displayed as lines:

row1: 0.

row2: 0.

Row3: 0.0.

Row 4: 0.0.

row 5: 0,0,0,0,0,0.

row6: -1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0 , 0, 0, – 1, 0, 0, 0, 0, 0, 1, 0.

row7: 2, 0, 0, 0, 0, 0, -2, 0, 0, 0, -2, 0, -2, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0 , 2, 0, 0, 0, 0, 0, -2, 0.

The line lengths are given by https://oeis.org/A058250.

Example of calculating the values ​​of line 6:

For the prime number 2 * 3 * 5 * 7 * 11 = 2310, which has 480 totals (480 percentages of 2310 <2310), the specified ranges are given by 480/2310. 480/2310 in reduced fraction = 16/77. Creating a set of GCD (2310 480) = 30 fractions by adding respectively 16 and 77 to the numerator and the denominator of the reduced fraction 16/77, we obtain the 30 fractions (only 9 are indicated):
16/77, 32/154, 48/231, 64/308, 80/385, 96/462, 112/539, 464/2233, 480/2310. Calculation of the totals of 2310 that are smaller and closer to each of the 30 denominators (only 9 displayed): 77,154,231,308,385,462,539, …, 2233,2310. gives the 30 totals (only 9 displayed):

73,151,229,307,383,461,533, … 2231,2309.

In the list of 480 totals out of 2310, these values ​​are 17, 32, 48, 64, 80, 96, 111, … the first total of 2310.

To generate row 6 values ​​from this, subtract the numerator from the 30 fractions of these values ​​(only 9 displayed):
(16-17), (32-32), (48-48), (64-64), (80-80), (96-96), (112-111), … (464-463) (480-480).

row 6: -1,0,0,0,0,0,1, … 1,0.

The 30 complete values ​​of row 6:
-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0 , 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0.

Also interested in the sums of the lines and non-zero value locations on the lines, ie the sum of the values ​​on a line = 0 always, I think. The non-zero values ​​of rows 6 and 7 are as follows: 1,7,11,13,17,19,23,29.

For row 5, use the prime number 2 * 3 * 5 * 7 = 210, which has 48 totals (48 coprimes of 210 <210). Creating a set of GCDs (210,48) = 6 fractions by adding 8 and 35 respectively to the numerator and the denominator of the reduced fraction 8/35 gives: 8/35, 16/70, 24/105, 32/140, 40 / 175, 48/210. Find the totals of 210 that are smaller and closer to each of the denominators: 35,70,105,140,175,210. gives the totals: 31,67,103,139,173,209. Thank you.

For line 7, enter the number 2 * 3 * 5 * 7 * 11 * 13 = 30030, consisting of 5760 totals (5760 areas 30030 <30030). Then create a set of GCDs (30030,5760) = 30 fractions, given by https://oeis.org/A058250.