The image is a pencil and watercolor drawing on a textured white paper. It features a woman with long, flowing yellow hair, sitting on the ground with her hands clasped together in a prayerful pose. She is facing a large, abstract blue shape that resembles a wave or a rock formation, with a tree growing from it. The background includes a few birds in flight and a soft, dreamy landscape with purple hues. The woman's face is not detailed, with a simple outline and a hint of red for her lips. The signature "Frank 25" is visible in the bottom left corner. The overall style is whimsical and ethereal, with a focus on soft lines and gentle colors.
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Zwei Schüler der Johanna-Tesch-Schule in Frankfurt wurden ohne Vorwarnung in den Osterferien ausgeflogen. Die Schülerschaft ist empört - und hat Angst.
TIL about the “Fermi-Dirac primes”, which mostly aren’t primes, and which AFAIK neither Fermi nor Dirac took any interest in. Ramanujan was interested in them, but he certainly didn’t name them this way, as Dirac was only 18 when Ramanujan died.
The Fermi-Dirac primes are integers that are primes raised to a power that is in turn a power of 2, i.e. p^{2^k}.
In order, they are:
2, 3, 4, 5, 7, 9, 11, 13, 16, ...
Every positive integer can be factored uniquely into a product of powers of primes, with no restriction on the powers of each prime.
But every positive integer can also be factored uniquely into a product of Fermi-Dirac primes, with each FDP appearing *at most once* in the product. Hence the name: the factors here are analogous to particles obeying Fermi-Dirac statistics, where each quantum state is occupied by either 0 or 1 particles, no more.
For example:
56 = 2^3 × 7 = 2^1 × 2^2 × 7 = 2 × 4 × 7
Ramanujan proved that the smallest number with exactly 2^k divisors is the product of the first k FDPs. For example:
2 × 3 × 4 × 5 × 7 × 9 = 7560
is the smallest number with exactly 2^6 = 64 divisors (including 1 and itself), and you can enumerate them simply by forming all 2^6 products that either include or omit each of those six FDPs.
Interesting. The fact that every number can be factored in FD primes is easy to see, since the normal primes are a subset of the FD primes (as p^{2^0}). And since any natural number can be expressed as the sum of powers of 2 (this is the base^* of the binary number system), we can decompose whatever power of p is needed into the product of different powers of 2. Nice!
Huh. This is so *almost* but not quite related to some of the stuff I was poking around recently--constructible regular polygons, particularly. (The odd-sided ones have numbers of sides whose prime factorizations are square-free, with unique primes of the form 2^(2^n) + 1. But those really have to be primes.)
The code for generating these in OEIS looks slow and bad, but if you have a streaming generator for the usual primes, then the Fermi–Dirac primes are easy to generate in sorted order: just merge the primes and the squares of the recursively generated Fermi–Dirac primes.
🗓️ Dimanche 18 mai à 18 h au port du Rosmeur (#Douarnenez).
"Gaza aujourd'hui : 18 mois de bombardements israéliens, une population palestinienne fracassée et affamée, au moins 55 000 victimes, d'innombrables blessés et disparus, un territoire ravagé dans le silence complice des états du monde entier, voire en aide active à l'agresseur.
Le collectif #Palestine Douarnenez crie ÇA SUFFIT !
Das Bild zeigt eine Instagram-Post von "comey" mit einem Foto von Sand, auf dem die Zahlen "8647" aus verschiedenen Muscheln und Steinen gebildet sind. Die Zahlen sind in verschiedenen Farben und Größen von Muscheln und Steinen angeordnet, die auf dem Sand liegen. Der Hintergrund besteht aus weichem, grauem Sand mit einigen Fußabdrücken und kleinen Steinen. Die Muscheln und Steine sind in verschiedenen Farben, darunter Braun, Grau und Schwarz. Der Text des Posts lautet: "comey Cool shell formation on my beach walk 1 hour ago" und zeigt 71 Likes.
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📷 A diferencia de lo habitual, hoy no traigo una foto de paisaje/arquitectura urbana. Eran las fiestas del barrio y nos habíamos juntado una pequeña multitud en los huertos urbanos. Creo que la foto refleja bien el ambiente festivo del día.
Tragica esplosione di gas nella villetta a Molazzana. Il giudice nomina i periti per fare luce sulle cause Il Gip Simone Silvestri ha nominato ieri i periti incaricati di far luce sulle responsabilità della tragica esplosione della villetta...
Wadephuls Vorstoß sorgt für Unruhe. Klingbeil mahnt zu Zurückhaltung bei Aussagen über die Höhe der Verteidigungsausgaben. Die Nato-Debatte spitzt sich zu.
Commanders in the Zionist enemy army acknowledged the difficulty of the ongoing battles in eastern Gaza City, especially in the Shujaiya neighbourhood, pointing out that Hamas fighters have adopted more sophisticated and effective tactics in the fiel…
Президент США Дональд Трамп у найближчі дні може звʼязатись із російською стороною, аби визначити подальші кроки для наближення завершення війни Росії проти України.
Yesterday, after work, cycling brought me to backwater villages, not hard to reach, but away from the usual flow of traffic. When I saw this house in the village of Weinsbach I stopped. The 1970s have been unapologetically retained, the style frozen in time, left to the weather like a forgotten monument. #Germany #photography #countryside
A Fujifilm Instax Mini 12 traz foco automático, modo close-up e espelho para selfies; conheça os principais recursos da câmera instantânea mais popular do momento
If the article's intent was to let the facts speak for themselves, it forgot to invite them. Instead, Tracy leveraged the full weight of his employer, America's paper of record, to ask an entertainer who sings with Elmo about how to go to school if she would care to comment about receiving money from Hamas. Nasty work.
The house style of the New York Times is severely outdated. Depending on the topic, the newspaper’s purportedly impartial tone instead reads as smug, self-amused, and deeply lazy.
Trump says “nothing happens” on Ukraine until he meets Putin. While Europe pushes for sanctions after failed talks, Trump stalls, leaving allies guessing — again. No pressure on the Kremlin.
mstdn.social/@noelreports/1145… It seems that the only option is to send a very clear invite to Putin. Drop the bridge. Europe needs to help by providing some of the means to do it. Putin may realize that his game is over when that happens.
Trump says “nothing happens” on Ukraine until he meets Putin. While Europe pushes for sanctions after failed talks, Trump stalls, leaving allies guessing — again. No pressure on the Kremlin.
Het succesvolste album van Dire Straits, Brothers in Arms, bestaat deze maand 40 jaar. Frontman Mark Knopfler vertelt hoe de plaat ook het begin van het einde was voor de succesvolle band.
i know, trump is taking too much of my attention already and i'm not even us-american. but once in a while i need the reminder that trump is not only horrible but also a clown: a real live horror clown. and then i feel somewhat lucky i don't live in the usa and feel very much afraid because the usa are very contagious.
Profitez des vidéos et de la musique que vous aimez, mettez en ligne des contenus originaux, et partagez-les avec vos amis, vos proches et le monde entier.
By Palestine Chronicle Staff More than 100 Palestinians were killed, injured, or remain missing following heavy Israeli airstrikes on northern Gaza’s residential areas and medical services. At dawn on Friday, Israeli forces launched a [...]
By Palestine Chronicle Staff UN agencies say famine is imminent in Gaza, with food and medicine stuck just minutes from the border. The World Health Organization (WHO) issued an urgent warning on Thursday about [...]
Arsenal Football Club is facing legal action after firing long-serving equipment manager Mark Bonnick after he expressed solidarity with Palestine on social media.
Why are people asking this questions? Trump is a Russian asset. Look here (sorry - it is in German)
Putins Helfer, Trump und Musk?
ZDF-Korrespondent Johannes Hano stieß bei seinen neuesten Recherchen auf bislang unbekannte und brisante Zusammenhänge zwischen den einstigen Gegnern USA und Russland.
MIT says it no longer stands behind a widely circulated research paper by its student that claimed an AI tool boosted discoveries in a materials science lab (Justin Lahart/Wall Street Journal)
Thomas' 'Hamlet' is a grand opera in five acts with a libretto by Michel Carré and Jules Barbier based on a French adaptation by Alexandre Dumas, père, and Paul Meurice of William Shakespeare's play Hamlet. Performers:
Charles Rice: H...
Rockchip Open-Source NPU Driver "RKNN" Continues Making Progress
Started just over one year ago was the effort to create an open-source Rockchip NPU driver. While not yet mainlined to the Linux kernel, progress on this kernel driver and associated user-space driver continues... phoronix.com/news/Rockchip-NPU…
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in reply to Frank DeTeEs • • •The image is a pencil and watercolor drawing on a textured white paper. It features a woman with long, flowing yellow hair, sitting on the ground with her hands clasped together in a prayerful pose. She is facing a large, abstract blue shape that resembles a wave or a rock formation, with a tree growing from it. The background includes a few birds in flight and a soft, dreamy landscape with purple hues. The woman's face is not detailed, with a simple outline and a hint of red for her lips. The signature "Frank 25" is visible in the bottom left corner. The overall style is whimsical and ethereal, with a focus on soft lines and gentle colors.
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