mathematics

Hans Riesel

Hans Riesel is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hans Riesel rather than just read about it. In short: Hans Ivar Riesel (28 May 1929 in Stockholm – 21 December 2014) was a Swedish mathematician who discovered the 18th Mersenne prime in 1957 using the computer BESK: 23217-1, comprising 969 digits. He held the record for the largest known prime from 1957 to 1961, when Alexander Hurwitz discovered a larger one.

Key takeaways

Hans Riesel belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hans Riesel to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hans Riesel from memory before moving on to harder problems.

Reference excerpt

Hans Ivar Riesel (28 May 1929 in Stockholm – 21 December 2014) was a Swedish mathematician who discovered the 18th Mersenne prime in 1957 using the computer BESK: 23217-1, comprising 969 digits. He held the record for the largest known prime from 1957 to 1961, when Alexander Hurwitz discovered a larger one. Riesel also discovered the Riesel numbers as well as developing the Lucas–Lehmer–Riesel test. After having worked at the Swedish Board for Computing Machinery, he was awarded his Ph.D. from Stockholm University in 1969 for his thesis Contributions to numerical number theory, and in the same year joined the Royal Institute of Technology as a senior lecturer and associate professor.

Career and research After completing an engineering degree at Kungliga Tekniska högskolan (KTH) in 1953, Riesel joined the state-run BESK computer project. Using nights and weekends on the machine he coded a self-checking Lucas–Lehmer routine in machine language, feeding exponents from punched paper tape; on 24 September 1957 the program halted with a zero residue for p = 3,217, identifying 23217 − 1 (969 digits) as the largest known prime of the day. Intrigued by numbers that resist such searches, he proved in 1956 that there exist odd integers k for which k·2ⁿ − 1 is composite for every n ≥ 1, inaugurating the study of what are now called Riesel numbers. He later generalised the Lucas–Lehmer test to these sequences, publishing the Lucas–Lehmer–Riesel test in 1981; this test remains the work-horse algorithm for the PrimeGrid distributed-computing project. Appointed senior lecturer at KTH in 1969, Riesel launched Sweden's first graduate course on computational number theory and supervised nine PhD theses on fast modular arithmetic and discrete logarithms. His monograph Prime Numbers and Computer Methods for Factorization (Birkhäuser, 1985; 2nd ed. 1994) synthesised that course and became a standard reference for early RSA cryptosystem implementers. Outside academia he co-founded the non-profit Stockholm Computer Association, promoting open access to idle mainframe time for scientific projects. He retired in 1994 but continued to maintain the Riesel Sieve webpages, coordinating a volunteer effort that has eliminated all but ten candidate Riesel numbers below 10,000.

Selected publications Riesel, Hans (1994). Prime Numbers and Computer Methods for factorization. Progress in Mathematics. Vol. 126 (2nd ed.). Boston, MA: Birkhäuser. ISBN 0-8176-3743-5. Zbl 0821.11001.

References

External links Riesel's web page Obituary

Worked examples

Example 1 — a first encounter with Hans Riesel

Start with the simplest possible case. Write down what Hans Riesel claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hans Riesel before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hans Riesel ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hans Riesel

In research: Hans Riesel appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hans Riesel in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hans Riesel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1929 births, 2014 deaths, Academic staff of the KTH Royal Institute of Technology, so understanding it makes those chapters shorter.
In everyday life: Look for Hans Riesel outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hans Riesel in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hans Riesel means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hans Riesel out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hans Riesel in simple terms?

Why does Hans Riesel matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hans Riesel?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hans Riesel.