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Today's Topics:
1. Re: One for the Numerologists and Mystics... (sylvano)
2. UN Adopts Milestone Cybercrime Treaty (Stephen Loosley)
3. Re: One for the Numerologists and Mystics... (David)
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Message: 1
Date: Wed, 01 Jan 2025 12:57:09 +1100
From: sylvano <[email protected]>
To: [email protected]
Subject: Re: [LINK] One for the Numerologists and Mystics...
Message-ID:
<[email protected]>
Content-Type: text/plain; charset="UTF-8"
Happy New Year, everyone!
One of the perplexity results doesn't add up:
**Sum of Consecutive Primes**
Interestingly, 2025 can be represented as the sum of five consecutive
prime numbers: 397 + 401 + 409 + 419 + 421 = 2025[7]. This connection
to prime numbers adds to its number-theoretical significance.
397 + 401 + 409 + 419 + 421 = 2047
Sylvano
On Tue, 2024-12-24 at 21:25 +1100, Antony Barry wrote:
> On Tue, Dec 24, 2024 at 9:05?PM David <[email protected]>
> wrote:
>
> > * 2025, itself is a square, i.e. 45 x 45 = 2025
> > * it is also a product of two-squares, i.e. 9? x 5? = 2025
> > * it is also the sum of 3-squares, i.e. 40?+ 20?+5?= 2025
> > * and remarkably it is also the sum of the cubes, of all the
> > single
> > digits, from 1 to 9, i.e.1?+2?+3?+4?+5?+ 6?+7?+8?+9?= 2025.
>
> I asked Perplexity AI is there was anything interesting about 2025
> with the
> following result -
>
> 2025 indeed possesses several interesting properties that make it
> noteworthy in number theory:
>
> ## Mathematical Properties
>
> **Perfect Square**
> 2025 is a perfect square, specifically 45^2[1][4]. This property
> alone
> makes it significant in number theory, as square numbers often
> exhibit
> unique characteristics.
>
> **Sum of Consecutive Odd Numbers**
> 2025 can be expressed as the sum of five consecutive single-digit odd
> natural numbers: 1 + 3 + 5 + 7 + 9[3]. This property is particularly
> interesting as it connects 2025 to other mathematical sequences.[Note
> by
> Tony: Perplexity seems to have got confused!]
>
> **Unique Squaring Property**
> 2025 is probably the only positive square which remains a square when
> adding 1 to each digit (resulting in 3136) as well as when increasing
> just
> the first digit (resulting in 3025)[2]. This unusual characteristic
> sets
> 2025 apart from other numbers.
>
> ## Number Theoretical Aspects
>
> **Prime Factorization**
> The prime factorization of 2025 is 3^4 * 5^2[1][6]. This
> decomposition into
> prime factors is fundamental in number theory and contributes to many
> of
> its other properties.
>
> **Divisibility**
> 2025 has 15 divisors[1], making it a highly composite number. It is
> also a
> tau number, as it is divisible by the number of its divisors[2].
>
> **Special Number Classifications**
> 2025 falls into several interesting number categories:
> - It is a Harshad number (divisible by the sum of its digits)[2].
> - It is a Curzon number[2].
> - It is an apocalyptic number[2].
> - It is a gapful number (divisible by the number formed by its first
> and
> last digit)[2].
>
> ## Unique Representations
>
> **Sum of Squares**
> 2025 can be written as a sum of two non-zero squares in only one way:
> 27^2
> + 36^2[2]. This property relates to the Pythagorean theorem and
> Fermat's
> theorem on sums of two squares.
>
> **Sum of Consecutive Primes**
> Interestingly, 2025 can be represented as the sum of five consecutive
> prime
> numbers: 397 + 401 + 409 + 419 + 421 = 2025[7]. This connection to
> prime
> numbers adds to its number-theoretical significance.
>
> ## Conclusion
>
> These properties collectively make 2025 a number of considerable
> interest
> in number theory. Its status as a perfect square, its unique
> representations as sums of consecutive numbers (both odd and prime),
> and
> its various special number classifications demonstrate that 2025
> possesses
> a rich set of mathematical characteristics worthy of study in number
> theory.
>
> Sources
> [1] Properties of the number 2025 - Number Empire
> https://www.numberempire.com/2025
> [2] Properties of number 2025 - Numbers Aplenty
> https://www.numbersaplenty.com/2025
> [3] 25 (number) - Wikipedia https://en.wikipedia.org/wiki/25_(number)
> [4] Number 2025 - Math Tools https://math.tools/numbers/2025
> [5] Properties of natural numbers such that there is a "very large
> largest
> ...
> https://mathoverflow.net/questions/101463/properties-of-natural-numbers-such-that-there-is-a-very-large-largest-number-w
> [6] Prime factors of 2025 - Math Tools
> https://math.tools/numbers/prime-factors/2025
> [7] Do you know this The number 2025 can be represented ... - Threads
> https://www.threads.net/@data.science.beginners/post/DD7WsWTTuaP
> [8] what is special about the number 2025? - hellosunday.ca
> https://hellosunday.ca/Vierte4/what-is-special-about-the-number-2025
>
> Tony
>
> >
--
sylvano
[email protected]
------------------------------
Message: 2
Date: Wed, 1 Jan 2025 13:58:00 +1100
From: Stephen Loosley <[email protected]>
To: [email protected]
Subject: [LINK] UN Adopts Milestone Cybercrime Treaty
Message-ID:
<sy5p282mb440916cae2850a7d7122051fc2...@sy5p282mb4409.ausp282.prod.outlook.com>
Content-Type: text/plain; charset=UTF-8; format=flowed
Please Note: This email did not come from ANU, Be careful of any request to buy
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important.
https://www.scamwatch.gov.au/types-of-scams/email-scams#toc-warning-signs-it-might-be-a-scam
UN General Assembly adopts milestone cybercrime treaty
A wide view of the General Assembly as it considered, for adoption, the
UN Convention against Cybercrime.
By Vibhu Mishra 24 December 2024 Law and Crime Prevention
https://news.un.org/en/story/2024/12/1158521
The General Assembly on Tuesday adopted the United Nations Convention
against Cybercrime, a landmark global treaty aimed at strengthening
international cooperation to combat cybercrime and protecting societies
from digital threats.
The agreement on the legally binding treaty marked the culmination of a
five-year effort by UN Member States, with inputs from civil society,
information security experts, academia and the private sector.
UN Secretary-General Ant?nio Guterres welcomed the adoption of the
Convention ? the first international criminal justice treaty to have
been negotiated in over 20 years.
http://www.undocs.org/A/79/460
?This treaty is a demonstration of multilateralism succeeding during
difficult times and reflects the collective will of Member States to
promote international cooperation to prevent and combat cybercrime,? his
spokesperson said in a statement.
The statement added that the Convention ?creates an unprecedented
platform for collaboration? in the exchange of evidence, protection for
victims and prevention, while safeguarding human rights online.
?The Secretary-General trusts that the new treaty will promote a safe
cyberspace and calls on all States to join the Convention and to
implement it in cooperation with relevant stakeholders.?
New tool to protect people
Phil?mon Yang, President of the General Assembly, highlighted the
importance of the new Convention.
?We live in a digital world, one where information and communications
technologies have enormous potential for the development of societies,
but also increases the potential threat of cybercrime,? he said.
?With the adoption of this Convention, Member States have at hand the
tools and means to strengthen international cooperation in preventing
and combating cybercrime, protecting people and their rights online.?
The resolution containing the Convention was adopted without a vote by
the 193-member General Assembly.
A victory for multilateralism
Ghada Waly, Executive Director of the UN Office on Drugs and Crime
(UNODC) also described the adoption of the treaty as a ?major victory?
for multilateralism.
?It is a crucial step forward in our efforts to address crimes like
online child sexual abuse, sophisticated online scams and money
laundering,? she said.
Ms. Waly reiterated the UN agency?s commitment to support all nations in
signing, ratifying and implementing the new treaty, as well as providing
them with the tools and support they need to protect their economies and
safeguard the digital sphere from cybercrime.
The Convention
The Convention against Cybercrime acknowledges the significant risks
posed by the misuse of information and communications technologies
(ICT), which enable criminal activities on an unprecedented scale,
speed, and scope.
It highlights the adverse impacts such crimes can have on States,
enterprises, and the well-being of individuals and society, and focuses
on protecting them from offenses such as terrorism, human trafficking,
drug smuggling and online financial crimes.
It also recognises the growing impact of cybercrime on victims and
prioritises justice, especially for vulnerable groups. It further
underscores the need for technical assistance, capacity-building and
collaboration among States and other stakeholders.
Read more about why the Convention against Cybercrime matters in this
explainer ..
https://news.un.org/en/story/2024/12/1158526
Next steps
The Convention against Cybercrime will open for signature at a formal
ceremony to be hosted in Hanoi, Viet Nam, in 2025. It will enter into
force 90 days after being ratified by the 40th signatory.
--
------------------------------
Message: 3
Date: Thu, 02 Jan 2025 11:35:37 +1100
From: David <[email protected]>
To: [email protected], sylvano <[email protected]>
Subject: Re: [LINK] One for the Numerologists and Mystics...
Message-ID: <8469556.T7Z3S40VBb@ulysses>
Content-Type: text/plain; charset="iso-8859-1"
On Wednesday, 1 January 2025 12:57:09 PM AEDT sylvano wrote:
> One of the perplexity results doesn't add up:
>
> **Sum of Consecutive Primes**
> Interestingly, 2025 can be represented as the sum of five consecutive
> prime numbers: 397 + 401 + 409 + 419 + 421 = 2025[7]. This connection
> to prime numbers adds to its number-theoretical significance.
>
>
> 397 + 401 + 409 + 419 + 421 = 2047
However I notice the sum of the first five prime numbers beginning one prime
earlier (389) does add up to 2015, thus: 389 + 397 + 401 + 409 + 419 = 2015
and the difference (10) can easily be found by differencing nearby primes.
It would be interesting to know if this erroneous result reflects some internal
glitch in Perplexity's architecture, and how it arose.
And my best wishes to Linkers for a peaceful, if interesting, 2025 whatever
its' numerical significance! I'd like to live for the next 100 years just to
see how it all turns out....
_David Lochrin_
------------------------------
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