Charles Weibel's Home Page

The 48th annual Almgren "Mayday" Race was held in the rain on May 5, 2024.
There were 7 teams, and NYU Math won with a time of 2:50.
Rutgers Math came in second.
The next race will be Sunday May 4, 2025, from Princeton to Rutgers.

Teaching Stuff (for more information, see Rutgers University, the Rutgers Math Department, and its Graduate Math Program.

Research papers & stuff: This is a link to some of my research papers.
Here are my research interests and my Ph.D. Students.

Do you like the History of Mathematics? Here are some articles:

I am often busy editing the Journal of Pure and Applied Algebra (JPAA), the Annals of K-theory and the journals HHA and JHRS.

Seminars I like:
Links to other WWW sites
Fun Question: How can you prove that 123456789098765432111 is a prime number?
note that 12345678987654321 = 111111111 x 111111111

Fun Facts about Mersenne primes: In 1644, a French monk named Marin Mersenne studied numbers of the form N=2p-1 where p is prime, and published a list of 11 such numbers he claimed were prime numbers (he got two wrong). Such prime numbers are called Mersenne primes in his honor. The first few Mersenne primes are 3,7,31,127 (corresponding to p=2,3,5,7), The next few Mersenne primes are 8191, 131071, 524287 (for p=13,17,19). (Each prime N=2p-1 has p log10(2) digits.)
Not all numbers of the form 2p-1 are prime; Regius discovered in 1536 that p=11 gives the non-prime 2047=23*89. The next few primes p for which 2p-1 is not prime are p=23 and p=37 (both discovered by Fermat in 1640), and p=29 (discovered by Euler in 1738).
Mersenne primes are the largest primes we know.
The largest known prime is the 51st Mersenne prime, with p=82,589,933; it has over 24 million digits and was discovered by an IT professional in December 2018. The next largest known prime is the 50th Mersenne prime, discovered in December 2017 using a Tennessee church computer; it has 23 million digits and p=77,232,917. Other recently discovered Mersenne primes are the 49th (2016) with 22 million digits and p=74,207,281; the 48th (2013) with 17 million digits and p=57,885,161; and the 47th, which has 13 million digits and p=43,112,609.

For years, the Electronic Frontier Foundation (EFF) offered a $50,000 prize for the first known prime with over 10 million digits; the 44th had 9.8 million digits and p=32,582,657. The race to win this prize came down the wire in Summer 2008, as the 45th and 46th known Mersenne primes were discovered in within 2 weeks of each other by the UCLA Math Department (who won the prize) and an Electrical Engineer in Germany, respectively. (The 46th had p=42,643,801 and the 45th has p=37,156,667.)
For more information, check out the Mersenne site.

Charles Weibel / weibel @ / July, 2021

HTML 4 font rendering:   ∂y/∂t = ∂y/∂x   √2 =1.414
If f(t)= ∫t 1 dx/x then f(t) → ∞ as t → 0. This really means:   (∀ε ∈ℝ,  ε>0) (∃δ>0) f(δ) > 1/ε .
ℕ (natural numbers), ℤ (integers), ℚ (rationals), ℝ (reals), ℂ (complexes)
The ndash (–) is & #150; ,   & #8211; and & ndash; !   I prefer the longer —, which is & mdash; or & #151;.