In short, my question is:

What percentage of American adults know what a prime number is?

Since this question is very specific, and my interests are a bit broader, I'd also be happy with:

Is there a good source for statistics on adult mathematical literacy? I have in mind things like knowledge of basic abstract mathematical concepts, like divisibility, primality, etc. I'm less interested in practical knowledge (interpreting graphs, statistics, that sort of thing).

Let me give some motivation for this question. When writing "popularly accessible" mathematics, I'd like to know something about my audience's background; it's also useful to have some idea of the average person's background when discussing math with a layperson. But I've had a lot of trouble finding statistics about people's knowledge of basic mathematical concepts, and people I've asked have given wildly different estimates of the answer to the question above.

So I'm looking for some reliable information, e.g. in the form of a poll. Of course I would also appreciate statistics about other countries, or sources of data of this type.

A good answer would be numerical data about this question or a similar one.

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    $\begingroup$ I don't know that there's a legit poll on this, but I'd bet the answer is 1/e. $\endgroup$ – JoeTaxpayer Apr 22 '14 at 2:05
  • $\begingroup$ It is certainly an interesting question, and I hope you get an answer. Another question that might helpful to such writers: what percentage of the general population is interested to read "popularly accessible" mathematics? If the answer to one is 50%, and the answer to the other is 50%, but the sets don't overlap, this is a problem! $\endgroup$ – JPBurke Apr 22 '14 at 2:07
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    $\begingroup$ What is your goal with this writing? Do you want to maximize your royalties? To maximize American understanding of the definition of a prime number? To promote your favorite theorem among the widest audience that would appreciate it? Your goal might determine your audience clearly enough that you won't need to rely on published polls. $\endgroup$ – user173 Apr 22 '14 at 2:32
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    $\begingroup$ Oh, I'd guess about $5\%$, since that's about $1/\operatorname{ln}(\text{US population})$. $\endgroup$ – Alexander Gruber Apr 22 '14 at 3:19
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    $\begingroup$ I'd think "prime numbers" are (at least informally) discussed in elementary school... $\endgroup$ – vonbrand Apr 22 '14 at 12:02

I don't see any studies of this sort on prime numbers, though I'm sure you could conduct an informal one and get a good estimate relatively quickly. Instead, I tackle your final note:

A good answer would be numerical data about this question or a similar one.

How about: Is zero even?

Citing a popular media piece:

According to Dr James Grime of the Millennium Maths Project at Cambridge University, reaction time experiments in the 1990s revealed people are 10% slower at deciding whether zero is odd or even than other numbers.

Children find it particularly difficult to recognise if zero is odd or even. "A survey of primary school children in the 1990s showed that about 50% thought zero is even, about 20% thought it was odd and the remaining 30% thought it was neither, both, or that they don't know," explains Dr Grime.

And it gets worse:

It's not just the public who have struggled to recognise zero as an even number. During the smog in 1977 in Paris, car use was restricted so that people with licence plates ending in odd or even numbers drove on alternate days.

"The police did not know whether to stop the zero-numbered licence plates and so they just let them pass because they didn't know whether it was odd or even," says Dr Grime.

As for primes: Are you wondering about the percentage of people who can precisely define when a number is prime? If so, I think asking them if $0$ or $1$ is prime is probably enough to reduce this number down to something miniscule.

(Consider this popular media piece on the polymath project post-Zhang, in which the author writes: Over the past year, mathematicians have been battling it out in a game involving primes, numbers that are only divisible by themselves and 1. Even allowing for "numbers" to refer to natural numbers, this definition would still include 1 as a prime.)

In any event, I think it is nice when popular media pieces on mathematics start with some basic definitions. I don't even think it's a stretch to include a definition of prime numbers in a graduate textbook on number theory.

In the most recent issue of the AMM, there is an article entitled The primes that Euclid forgot (link). Though 'prime' is not explicitly defined, 'quadratic residue' is: see the start of section two. Of course, this latter term is sure to be quite unfamiliar to the general populace; but I expect it is known by a very large proportion of the American Mathematical Monthly's readership. If the authors there feel including a reminder-definition is worthwhile, then I suggest you dedicate a line to defining the term 'prime' in any relevant popular media piece.

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    $\begingroup$ An interesting collection of facts, but my mind is literally boggled trying to imagine in what sense you might think it answers the question. $\endgroup$ – jwg Apr 22 '14 at 9:51
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    $\begingroup$ This answers the implied underlying question "Should I define prime in my popular mathematics article." $\endgroup$ – Chris Cunningham Apr 22 '14 at 10:36
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    $\begingroup$ This is somewhat ufair, as 0 and 1 are certainly very special. AFAIU, 1 was considered "prime" almost universally up to not so long ago. $\endgroup$ – vonbrand Apr 22 '14 at 12:03
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    $\begingroup$ @jwg The OP concludes: I'm looking for some reliable information, e.g. in the form of a poll. Of course I would also appreciate statistics about other countries, or sources of data of this type. A good answer would be numerical data about this question or a similar one. Unfortunately, I could not find any information about a survey on prime number familiarity; so: I provided some data about a similar question, namely, whether or not 0 is even. Moreover, I tried to respond to address the OP's motivation insofar as writing popular math media pieces is concerned. $\endgroup$ – Benjamin Dickman Apr 22 '14 at 13:40
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    $\begingroup$ @jwg: I think this is a perfectly reasonable, if not conclusive, answer, which I've voted up. Not only that, it literally relates to the question--if one doesn't know which numbers divide zero, one doesn't understand the definition of "divisibility" and thus of the word "prime." $\endgroup$ – Daniel Litt Apr 22 '14 at 15:57

Opening section of this document refers to a number of studies of numeracy of US population. One of the major international efforts in providing standardized, comparable-across-countries data on adult literacy and numeracy skills is OECD's Programme for the International Assessment of Adult Competencies (PIIAC). The US country report is here; I know some of the authors through the professional circles, and can ask informally for details. The codebook (meta-data about questions) does not seem to have any questions about primes, but I would still need to see the specific instrument. You can even take the test yourself if you like, although the website only support Firefox (and declined to operate in my Chrome... ah well). Media outlets that reported on the study also reposted the typical questions. The single number that the media picked up is 9% of US adults ages 16 to 65 being proficient at the highest level. That will probably be the best answer to your question, lacking the specific study on knowledge of prime numbers.

  • $\begingroup$ Addressing the issue of numeracy was a main reason for my creating the content that I later deposited in my website of public-domain materials, at www.public-domain-materials.com $\endgroup$ – Mike Jones Aug 24 '14 at 14:21

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