Infinite Number of Primes (Euklid)

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In addition to reputation, you can receive badges for special achievements on the site. Badges are items you can show off in your public profile. Some badges are more easy to be earned than others. How easy (or difficult) it is to receive a badge is indicated by the number on the badge from 4 (easy) to 1 (difficult). You can receive the following badges:

Badges related to primary content (tell me more ») Primary content is any type of your contributions to the BoP's wiki, which are dedicated to "pure mathematics", i.e. definitions, mathematical statements, proofs or axioms. Each branch can be structured in chapters, sections and subsections. In order to gain badges, while contributing to primary content of any type, you should focus on mathematical correctness, preciseness and, in some cases, mathematical beauty.
	I'm a (co-)author of a branch subsection	I'm a (co-)author of a branch section	I'm a (co-)author of a branch chapter	I'm a (co-)author of a branch
	I contributed to a proof	I contributed a mathematical statement (proposition, lemma, theorem or corollary).	I contributed to a definition.	I contributed to an axiom.
Badges related to secondary content (tell me more ») Secondary content is any type of background information to "primary content" (see above). It comprises of motivations, examples, explanations or real-life applications of mathematics. When contributing this type of content you should focus on how understandable and useful your background information is rather than how rigorous it is from a mathematical point of view. In other words, it might be somewhat informal as long as it contributes to the understandability of the pure mathematics behind.
	I contributed at least 5 examples.	I contributed at least 5 explanations.	I contributed applications to at least 5 different topics.	I interpreted or provided motivations for at least 5 different topics.
	I contributed a new example.	I contributed a new explanation.	I contributed a new application.	I contributed a new interpretation or provided a new motivation to a topic.
Badges related to the history of mathematics
	I'm a (co-)author of a mathematician profile.	I'm a (co-)author of a historical note.	I contributed to at least 3 different profiles of mathematicians.	I contributed to at least 3 different historical notes.
Badges related to bibliography
	I contributed to at least 1 bibliography entry.	I contributed to at least 10 bibliography entries.	I contributed to at least 25 bibliography entries.	I contributed to at least 50 bibliography entries.
Badges related to profile popularity
	I created my public profile.	My profile has been viewed at least 10 times.	My profile has been viewed at least 100 times.	I'm popular (>1k views).
Badges related to community
	I accepted at least 10 postings of other users.	I rejected at least 3 postings of other users and was right!	I accepted at least 40 postings of other users.	I rejected at least 9 postings of other users and was right!

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What are badges?

Badges related to primary content (tell me more »)

Badges related to secondary content (tell me more »)

Badges related to the history of mathematics

Badges related to bibliography

Badges related to profile popularity

Badges related to community