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We are going to check if a number is prime.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.
Steps:
If the number is less than 2, it is not prime.
If the number is 2, it is prime.
If the number is even (and greater than 2), it is not prime.
Check for odd divisors up to the square root of the number.
However, note that 2 is the only even prime. So we can handle 2 separately and then check only odd numbers.
Let's write a function is_prime(n) that returns True if n is prime, else False.
To determine if a number is prime, we need to check whether it is greater than 1 and has no divisors other than 1 and itself. Here's a step-by-step explanation and implementation:
Approach
Check for numbers less than 2: These are not prime.
Check for 2: The smallest prime number.
Check for even numbers: Any even number greater than 2 is not prime.
Check odd divisors: For odd numbers, test divisibility by odd integers from 3 up to the square root of the number. If any divisor is found, the number is not prime.
Solution Code
import math
def is_prime(n):
if n < 2:
return False
if n == 2:
return True
if n % 2 == 0:
return False
for i in range(3, int(math.isqrt(n)) + 1, 2):
if n % i == 0:
return False
return True
Explanation
Initial Checks:
Numbers less than 2 are non-prime.
The number 2 is prime.
Even numbers greater than 2 are non-prime.
Divisibility Test:
For odd numbers starting from 3, check divisibility up to the integer square root of the number.
Increment by 2 to test only odd divisors (since even divisors would have been caught earlier).
If any divisor is found, return False immediately.
If no divisors are found, return True.
This approach efficiently checks for primality by leveraging mathematical properties (e.g., checking up to the square root) and skipping even divisors after handling the number 2. The complexity is (O(\sqrt{n})), which is optimal for this problem.
Okay, so I need to figure out what PRIME stands for here. The user just wrote "PRIME" and that's it. Hmm, maybe they want me to explain what PRIME means in different contexts? Let me start by thinking about common expansions of PRIME.
First, in mathematics, PRIME could refer to prime numbers, which are numbers greater than 1 that have no divisors other than 1 and themselves. But the acronym PRIME itself... Maybe it's an organization or a project? Let me check some possibilities.
In technology, there's the PRIME project by Intel, which is about power efficiency. Also, PRIME could stand for the Public Real-time Infrared Measurement Equipment. Or in medicine, PRIME might relate to a study or protocol. Wait, there's also the PRIME network in healthcare, which is a telehealth platform.
Another angle: in acronyms, sometimes each letter stands for a word. Let me think letter by letter. P could be "Professional," R "Resource," I "Integration," M "Model," E "Enterprise." Not sure. Alternatively, P might be "Private," R "Reliable," I "Medical," M "Exchange," E "Platform." That's a stretch.
Wait, maybe the user is referring to the PRIME algorithm? I recall there's something called the PRIME algorithm for generating prime numbers. Or PRIME in the context of the PRIME directive from Star Trek, which is "To boldly go where no man has gone before," but that's more of a cultural reference.
Alternatively, in the UK, PRIME stands for the People's Rail Industry Mailer, but that's pretty obscure. In finance, PRIME might be a type of account or service. For example, some banks have PRIME accounts for high-net-worth individuals.
Let me verify some of these. The PRIME project by Intel is indeed focused on power management. The PRIME network in healthcare is used for telemedicine. The PRIME algorithm is a method for prime number generation. The PRIME directive is a fictional concept from Star Trek. There's also PRIME in the context of the PRIME standard for financial services.
Since the user didn't specify a context, I should list the most common meanings. Let me structure this:
Mathematics: Prime numbers.
Technology: Intel's PRIME project for power efficiency.
Healthcare: PRIME network for telehealth.
Star Trek: The PRIME directive.
Finance: PRIME accounts or standards.
Academic: PRIME initiatives or research programs.
I should also mention that PRIME can be an acronym where each letter stands for a different word depending on the context. For example, in some contexts, it might stand for "Publicly Represented Interoperable Medical Environment."
Wait, maybe the user is referring to a specific PRIME acronym they encountered elsewhere. Without more context, it's hard to be precise. But covering the major areas should help. Let me check if there's a PRIME organization or standard I'm missing. There's also the PRIME certification for medical devices, or PRIME in the context of project management methodologies.
Alternatively, in the military, PRIME could be an acronym for a protocol or system. But I'm not sure. To ensure I'm not missing anything, I'll list the most probable ones and explain that context is key. That way, the user can clarify if needed.
PRIME can stand for various terms depending on the context. Here are some common interpretations:
Mathematics:
Prime Numbers: Numbers greater than 1 with no divisors other than 1 and themselves (e.g., 2, 3, 5, 7).
Technology:
Intel PRIME: A project focused on power-efficient computing technologies.
PRIME Algorithm: A method for generating prime numbers efficiently.
Healthcare:
PRIME Network: A telehealth platform used for remote medical consultations.
Cultural/Science Fiction:
PRIME Directive: From Star Trek, a fictional ethical guideline stating, "To boldly go where no man has gone before."
Finance:
PRIME Accounts: High-net-worth savings or investment accounts offered by some banks.
PRIME Standard: A certification for secure financial transactions.
Academic/Research:
PRIME Initiative: Various research programs, such as the PRIME project in mathematics (e.g., collaborative prime number research).
Other Acronyms:
Publicly Represented Interoperable Medical Environment (healthcare IT).
Power Resource Innovation for Maximum Efficiency (energy systems).
If you had a specific context in mind, feel free to clarify for a more targeted explanation!
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发表于 2025-11-10 06:17:34