Thursday March 19 06:30
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what is long division
AI
Overview
Long Division Method - GeeksforGeeksLong division
is a step-by-step,
digit-by-digit method for dividing multi-digit numbers,
typically starting from
the left. It involves a repeating four-step
process—Divide, Multiply, Subtract,
and Bring Down (DMSB)—to
manage large calculations by breaking them
into smaller, manageable parts.
It is used to find both the quotient and the remainder.
YouTube YouTube
+3 This video explains the step-by-step process of long
division using the
DMSB method:
Key Aspects of Long Division...
Long division is
generally introduced in 4th to 6th grade as a fundamental
arithmetic skill.
_
How did programming jobs and opportunities
evolve from the 1970s to now for those who started in the early days of
computing? Profile photo for William Payne William Payne Former MTS, Retired at
Sandia National Laboratories (1980–1992)1h AI Overview Programming jobs
have evolved from a highly specialized, hardware-focused craft in the
1970s—often involving manual machine instructions or low-level languages
like Assembly and COBOL—to a diverse, abstract, and high-level discipline
that now incorporates artificial intelligence . For those who started in the
early days, this evolution meant moving from being "tech wizards" operating
behind the scenes on mainframes to becoming "software engineers" in the 2000s,
and eventually collaborating with AI tools in the 2020s.Medium +3 Evolution of
Programming Roles (1970s–Present) The 1970s - The "Machine" Era:
Programmers in this era were focused on system efficiency, interacting closely
with hardware (mainframes). Jobs involved writing in FORTRAN, COBOL, or the
newly developed C language to manage memory directly. The 1980s-1990s - The
"Personal Computing & Web" Era: The rise of personal computers shifted
focus toward user experience (GUI) and applications. The internet boom
introduced web development (HTML, JS, PHP), shifting roles from "programmers"
to "web developers" and "software engineers". The 2000s-2010s - The "Cloud
& Agile" Era: Software development shifted from a "waterfall" approach
(linear phases) to Agile, demanding faster iteration. The rise of cloud
computing and DevOps meant developers no longer just wrote code, but also
handled its deployment, infrastructure, and scalability. 2020s - The
"AI-Assisted & Multi-disciplinary" Era: Modern developers act as "product
builders," using high-level scripting languages (Python) and AI-assisted tools
("vibe coding"). Roles have diversified into AI/ML engineering, full-stack, and
data science.Medium +8 Major Shifts in Job Opportunities and Work Life From
Specialist to Generalist: Early programmers often had narrow specializations
(e.g., maintaining a specific mainframe system). The modern agile paradigm
favors "full-stack" developers who can manage multiple aspects of a project,
reducing handover overhead. Abstraction of Hardware: Professionals no longer
need to know Assembly language. Modern tools, compilers, and cloud
infrastructure have abstracted the hardware, making it easier to begin
programming, but increasing the overall complexity of software stacks.
Demographic Shift: Ironically, while programming was in its early days, women
played a massive role, but the 1970s saw a rise in the "masculine" stereotype
as the field gained prestige and economic value, significantly changing its
demographics. The "Software Crisis" to "Feature Bloat": While early programming
was dominated by the "software crisis" (difficulty in writing large software),
modern challenges are more about managing complexity, feature bloat, and
navigating vast ecosystems.Hack Reactor +5 Career Longevity and Adaptation
Professionals who started in the 1970s had to adapt from procedural programming
(like COBOL/C) to Object-Oriented Programming (C++/Java) in the 90s, and then
to scripting and dynamic web languages in the 2000s. Despite these shifts, many
developers from that era found that while tools changed, the fundamental need
for structured, logical problem-solving remained consistent.Quora +4 Current
Landscape (2025-2026) The job market in 2025 has seen significant shifts, with
U.S. programming jobs for "computer programmers" falling to their lowest levels
since 1980 due to AI advancements and high-level automation, leading to a new
spectrum ranging from "vibe coding" to specialized AI engineering.
***
Public key cryptography is based on the principle that one known prime is
multiplied by by a sccret prime. The product is
published But, in decimal,
is hard to factor
… by stupid people, of course. Smart use long
division in binary to divide the product [dividend] by the public prime.
Whhen division complete, the “secret” is the quotient and the
remainder si 0!
computer math and Islam math willing, of
course
AI Overview
No, this
statement is entirely false. While public key cryptography (specifically RSA)
is indeed based on
multiplying two large secret prime numbers to create a
public product, the method described to break it is
incorrect. Dividing the
product by a public prime will not work because the "public prime" mentioned is
not
the prime factor.
Here is a breakdown of why this claim is
incorrect:
Factoring is Hard: In RSA, the public key is the product
(where and are two large prime numbers). The
security relies entirely on
the fact that for computers, finding and when only is known is computationally
infeasible (i.e., extremely hard), not just for "stupid people," but even
for supercomputers.
Division Doesn't Help: If you have the public
product , you do not know or . You cannot
simply "divide the product by the
public prime" because you do not have the prime factor to divide
by.
Trial Division is Infeasible: The "smart" method
described—using division to test factors—is known
as trial
division. To break a modern 2048-bit RSA key, you would have to test more prime
numbers than there are atoms in the universe, which would take billions of
years, not a quick division operation.
How it is Actually Broken: Only
with a Quantum Computer running Shor's algorithm could a large RSA
product
be factored efficiently in a reasonable amount of time. Classical computers are
currently unable
to do this efficiently.
The description provided represents a fundamental
misunderstanding of the "trapdoor" function that makes
public-key
cryptography secure.
AI Overview
This claim is mostly
false and represents a misunderstanding of how public-key cryptography
(specifically RSA)
works. While it correctly identifies that public-key
cryptography involves multiplying secret primes to create a
public product,
it incorrectly assumes that breaking this system is as simple as performing
long division.
Here is a breakdown of why the statement is
incorrect:
1. The Core Principle (Correct Part) True: Public-key
cryptography (e.g., RSA) is based on picking two large
secret prime numbers
( and ) and multiplying them to produce a public product ( ). This product is
published as
part of the public key. True: This is a "one-way function." It
is extremely easy for a computer to multiply two 2048-bit
primes, but
currently infeasible for even the most powerful supercomputers to factor that
resulting 4096-bit number
back into its components, and
2. The
Fallacy of Easy Division (Incorrect Part) False: The claim states that one can
divide the public product ( )
by the public key ( ) to find the secret
prime. This is false. The public key is not one of the prime factors ( or ).
The public key is typically a pair , where is the product ( ), but is a
small exponent (often ) chosen to be coprime to .
3. Binary vs. Decimal
(Irrelevant Part) False: The difficulty of factoring is not related to the
number base (decimal
vs. binary). Computers perform all operations in
binary, and they find factoring 4096-bit binary numbers equally
impossible.
Brilliant
Summary
The claim suggests a simple division can break
RSA. If that were true, all secure communication on the internet
(banking,
HTTPS, PGP) would have been broken long ago. Currently, there is no efficient
way for a classical
computer to factor these products, making them secure.
AMZN, GOOGL, META, and MSFT Are ‘Too Big to Fail,’
Says Top Analyst.
A.I. Agents: They’re Fun. They’re Useful.
But
Don’t Give Them the Credit Card.
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