prime numbers

Amazon's October Prime Day event has ended, but a number of discounted products remain on sale. Outlets are highlighting leftover deals that are still live, giving shoppers a second chance at savings. Coverage focuses on which reader-favorite items kept their discounted prices after the official sale window closed.

Prime Minister Narendra Modi expressed grief over the loss of lives in an accident in Kutch, Gujarat, offering condolences to the families of the deceased and wishing a swift recovery to the injured. The prime minister's office shared the message as details of the incident, including the number of casualties and its cause, remain limited.

A new paper establishes that the sum of reciprocals of prime-prefix-free numbers — integers that do not contain any prime as a prefix of their decimal representation — converges to a finite value. The result is notable because sets of integers avoiding prefix conditions often have divergent reciprocal sums, and it is drawing attention from mathematics enthusiasts debating the proof techniques and possible generalisations.

Italian Prime Minister Giorgia Meloni has announced a ban on face coverings in schools, alongside plans to cap the number of foreign students in each classroom. The measures, framed as protecting Italian students and their identity, sparked strong reactions online, with supporters praising the hard line and critics calling it discriminatory.

Amazon's October Prime Day sales event has ended, but Lifehacker reports that a number of smartwatch discounts are still live. The roundup highlights reduced prices on popular wearables that shoppers can still pick up, listing which models remain on sale and where the savings are. It is aimed at consumers who missed the event or want a second chance at deals on devices like the Apple Watch and other smartwatch brands.

Latvia's ruling party led by Prime Minister Andris Kulbergs won a record number of seats in the country's parliamentary elections, an outcome reported to strengthen his grip on power. Commentators note the result comes as Latvia and its Baltic neighbours face heightened security concerns tied to Russia, with voters widely seen as backing continuity in government.

A six-page graduate-level introduction has been published on the decomposition of increasing integer sequences into weight × level + jump, with the prime numbers presented as the main application. The text, released on decompwlj.com, is aimed at graduate students in number theory. Discussion is limited so far, with mathematicians sharing the primer in number theory circles.

A proposed decomposition of prime numbers into a formula of weight, level and jump restates the Twin Prime Conjecture in a new form: there are infinitely many primes with weight 3. The claim, shared alongside a visualization, suggests that if proven, this formulation would resolve the centuries-old conjecture about infinitely many twin primes. Mathematicians note such reformulations are intriguing but the underlying conjecture remains unproven.

Le Canard Enchaîné reports that Prime Minister Sébastien Lecornu was among the victims of a 2024 hack of a customer database of the French telecom company Le Slip Français... more precisely, his mobile phone number is now circulating on the Darknet, along with those of 25 of the 36 members of the government, following a breach of a client database. The revelation has raised questions about data security and the exposure of senior officials' personal contact details.

AWS has published figures on the infrastructure that powered Amazon Prime Day 2026, detailing the scale of traffic, compute capacity and transactions handled during the shopping event. The breakdown highlights the technical demands of running one of the world's largest retail events and the cloud systems behind it, drawing interest from developers and cloud watchers weighing the numbers for themselves.

A new paper proves that the reciprocal sum of the prime-prefix-free numbers converges, settling a question about this set of integers in which no number appears as a prefix of another when written out. The short PDF, shared on an author's personal page, is being passed around among mathematicians and programming enthusiasts interested in number theory.

A large pro-Imran Khan rally has been launched in Pakistan after negotiations between the government and the former prime minister's camp ended without agreement. Organisers called supporters to gather in mass numbers, deepening the political standoff. Khan remains a central figure in Pakistani politics, and the failed talks have raised tensions between his movement and state authorities.

The Pittsburgh Steelers-Cleveland Browns matchup drew 16.59 million viewers on Prime Video, a large audience for the NFL's streaming coverage. The figure highlights the league's continued ability to pull big crowds to exclusive streaming games, and fans are weighing in on what the numbers mean for the future of NFL broadcasts on platforms like Amazon.

An online mathematics project is assigning a SHA-256 hash to each of 5,000 integer sequences decomposed into a unique weight × level + jump form, verifying the decomposition at every deployment. Primes are among the sequences given cryptographic fingerprints, with Claude assisting in generating and checking the hashes, a hybrid of number theory and software integrity practice.

Betting odds for every NFL Week 5 matchup have been released, with the Dallas Cowboys, Baltimore Ravens and Los Angeles Rams installed as favorites in the primetime slots. The lines give early indicators of where oddsmakers see the advantages as the season reaches its fifth week, and fans and bettors are comparing the numbers against recent team form and injury reports.

A mathematical claim is circulating that the decomposition of natural numbers into weight × level + jump is equivalent to the sieve of Eratosthenes, the classical ancient Greek algorithm for finding prime numbers. The idea, shared under the shorthand decompwlj, is drawing attention among math enthusiasts discussing prime number generation methods.