Double-Struck Capital P

It is a mathematical letter whose role depends on the field.

In probability, ℙ marks a probability measure or an event's probability. In number theory it can stand for the prime numbers; in geometry, ℙⁿ commonly names projective space. Set theory also uses ℙ(S) for the power set of S, meaning all its subsets, though a cursive-style P is common there. The field and formula settle which reading fits.

Why is the P double-struck?

The double stroke began as a practical writing aid.

By the late 1950s, mathematicians used double strokes on blackboards and typewriters to make bold letters easier to tell apart. The style took hold in Princeton mathematics in the early 1960s, then entered printed notation and math fonts. Unicode keeps some familiar double-struck letters, including ℙ, as individual older symbols and encodes the broader mathematical alphabets separately.

What if someone sends ℙ without a formula?

Without its formula, ℙ has no single reliable conversational reading.

Treat it as a mathematical letter and ask for context. Probability, primes, and projective space are all possible in formulas; none is a safe guess from the glyph alone.