mathematics

Megaprime

Megaprime 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 Megaprime rather than just read about it. In short: A megaprime is a prime number with at least one million decimal digits. Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits (of which the smallest is 10999+7), and "gigantic prime" for a prime with at least 10,000 digits (of which the smallest is 109999+33603).

Key takeaways

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

Reference excerpt

A megaprime is a prime number with at least one million decimal digits. Other terms for large primes include "titanic prime", coined by Samuel Yates in the 1980s for a prime with at least 1000 digits (of which the smallest is 10999+7), and "gigantic prime" for a prime with at least 10,000 digits (of which the smallest is 109999+33603).

As of 1 January 2026, there are 3,797 known megaprimes which have more than 1,000,000 digits. The first to be found was the Mersenne prime 26972593−1 with 2,098,960 digits, discovered in 1999 by Nayan Hajratwala, a participant in the distributed computing project GIMPS. Nayan was awarded a Cooperative Computing Award from the Electronic Frontier Foundation for this achievement. Almost all primes are megaprimes, as the number of primes with fewer than one million digits is finite. However, the vast majority of known primes are not megaprimes. All numbers from 10999999 through 10999999 + 593498 are known to be composite, and there is a very high probability that 10999999 + 593499, a strong probable prime for each of 8 different bases, is the smallest megaprime. As of 2024, the smallest number known to be a megaprime is 10999999 + 308267×10292000 + 1. The last prime that is not a megaprime is currently unknown. As of 2024, the largest prime number known to not be a megaprime is 10999999 − 1022306×10287000 − 1. There is a very high probability that 10999999 − 172473 is the biggest non-mega prime.

See also List of largest known primes and probable primes, a list that includes the largest known megaprimes and probable megaprimes Largest known prime number Electronic Frontier Foundation § Awards

References

Illustrations

Worked examples

Example 1 — a first encounter with Megaprime

Start with the simplest possible case. Write down what Megaprime 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 Megaprime 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 Megaprime 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 Megaprime

In research: Megaprime 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 Megaprime 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: Megaprime is common in secondary-school and first-year university syllabi. It links to neighbouring topics Large integers, Prime numbers, so understanding it makes those chapters shorter.
In everyday life: Look for Megaprime 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 Megaprime in 20 minutes

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

Frequently asked questions

What is Megaprime in simple terms?

Why does Megaprime 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 Megaprime?

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 Megaprime.