mathematics

Ralph Ernest Powers

Ralph Ernest Powers 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 Ralph Ernest Powers rather than just read about it. In short: Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers. He is credited with discovering the Mersenne primes M89 and M107, in 1911 and 1914 respectively.

Key takeaways

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

Reference excerpt

Ralph Ernest Powers (April 27, 1875 – January 31, 1952) was an American amateur mathematician who worked on prime numbers. He is credited with discovering the Mersenne primes M89 and M107, in 1911 and 1914 respectively. In 1934 he verified that the Mersenne number M241 is composite.

Life Powers was born in Fountain, Colorado Territory. Details of his life are little-known, though he appears to have been an employee of the Denver and Rio Grande Western Railroad. Soon after Powers announced the discovery of M107, the Frenchman E. Fauquembergue claimed that he had discovered it earlier, but many of Fauquembergue's other claims were later demonstrated as erroneous; thus, many prefer recognizing Powers as the discoverer, including the well-known Internet resource the PrimePages. After his own discoveries of Mersenne primes in 1911 and 1914, no Mersenne primes were discovered until Raphael M. Robinson used a computer to find the next two, on January 30, 1952, the night before Powers's death.

Works ‘The Tenth Perfect Number', American Mathematical Monthly, Vol. 18 (1911), pp. 195–7 ’On Mersenne's Numbers', Proceedings of the London Mathematical Society, Vol. 13 (1914), p. xxxix 'A Mersenne Prime', Bulletin of the American Mathematical Society, Vol. 20, No. 10 (1914), p. 531 ’Certain composite Mersenne's numbers', Proceedings of the London Mathematical Society Vol. 15 (1916), p. xxii (with D. H. Lehmer) 'On Factoring Large Numbers', Bulletin of the American Mathematical Society, Vol. 37. No. 10 (1931), pp. 770–76 ’Note on a Mersenne Number', Bulletin of the American Mathematical Society, Vol. 40, No. 12 (1934), p. 883

See also Continued fraction factorization

References

External links The Prime Pages website Mersenne and Fermat Numbers (Robinson); brief treatment of Powers The Tenth Perfect Number, an article by Powers announcing the primality of M89

Worked examples

Example 1 — a first encounter with Ralph Ernest Powers

Start with the simplest possible case. Write down what Ralph Ernest Powers 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 Ralph Ernest Powers 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 Ralph Ernest Powers 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 Ralph Ernest Powers

In research: Ralph Ernest Powers 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 Ralph Ernest Powers 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: Ralph Ernest Powers is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1875 births, 1952 deaths, American mathematician stubs, so understanding it makes those chapters shorter.
In everyday life: Look for Ralph Ernest Powers 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Ralph Ernest Powers” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Ralph Ernest Powers in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Ralph Ernest Powers 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 Ralph Ernest Powers out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Ralph Ernest Powers in simple terms?

Why does Ralph Ernest Powers 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 Ralph Ernest Powers?

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 Ralph Ernest Powers.