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class="ab cb"><div class="ci bh fz ga gb gc"><div><h1 id="c824" class="pw-post-title gs gt gu bf gv gw gx gy gz ha hb hc hd he hf hg hh hi hj hk hl hm hn ho hp hq hr hs ht hu bk" data-testid="storyTitle">In Wolfram Mathematica, you can have two pure functions on one line</h1><div><div class="speechify-ignore ab cp"><div class="speechify-ignore bh l"><div class="hv hw hx hy hz ab"><div><div class="ab ia"><div><div class="bm" aria-hidden="false"><a rel="noopener follow" href="/?source=post_page---byline--bd892d16c411--------------------------------"><div class="l ib ic by id ie"><div class="l fj"><img alt="Alonso Del Arte" class="l fd by dd de cx" src="https://miro.medium.com/v2/resize:fill:88:88/0*FBroauQs7X1lETSC." width="44" height="44" loading="lazy" data-testid="authorPhoto"/><div class="if by l dd de fs n ig ft"></div></div></div></a></div></div></div></div><div class="bn bh l"><div class="ab"><div style="flex:1"><span class="bf b bg z bk"><div class="ih ab q"><div class="ab q 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mn mo mg mh paragraph-image"><div role="button" tabindex="0" class="mp mq fj mr bh ms"><div class="mg mh mi"><picture><source srcSet="https://miro.medium.com/v2/resize:fit:640/format:webp/0*5-qcxFuaAx96d-9W 640w, https://miro.medium.com/v2/resize:fit:720/format:webp/0*5-qcxFuaAx96d-9W 720w, https://miro.medium.com/v2/resize:fit:750/format:webp/0*5-qcxFuaAx96d-9W 750w, https://miro.medium.com/v2/resize:fit:786/format:webp/0*5-qcxFuaAx96d-9W 786w, https://miro.medium.com/v2/resize:fit:828/format:webp/0*5-qcxFuaAx96d-9W 828w, https://miro.medium.com/v2/resize:fit:1100/format:webp/0*5-qcxFuaAx96d-9W 1100w, https://miro.medium.com/v2/resize:fit:1400/format:webp/0*5-qcxFuaAx96d-9W 1400w" sizes="(min-resolution: 4dppx) and (max-width: 700px) 50vw, (-webkit-min-device-pixel-ratio: 4) and (max-width: 700px) 50vw, (min-resolution: 3dppx) and (max-width: 700px) 67vw, (-webkit-min-device-pixel-ratio: 3) and (max-width: 700px) 65vw, (min-resolution: 2.5dppx) and (max-width: 700px) 80vw, 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(max-width: 700px) 80vw, (-webkit-min-device-pixel-ratio: 2.5) and (max-width: 700px) 80vw, (min-resolution: 2dppx) and (max-width: 700px) 100vw, (-webkit-min-device-pixel-ratio: 2) and (max-width: 700px) 100vw, 700px"/><img alt="" class="bh ln mt c" width="700" height="467" loading="eager" role="presentation"/></picture></div></div><figcaption class="mu ff mv mg mh mw mx bf b bg z du">Photo by <a class="af my" href="https://unsplash.com/@antoine1003?utm_source=medium&amp;utm_medium=referral" rel="noopener ugc nofollow" target="_blank">Antoine Dautry</a> on <a class="af my" href="https://unsplash.com/?utm_source=medium&amp;utm_medium=referral" rel="noopener ugc nofollow" target="_blank">Unsplash</a></figcaption></figure><p id="64a4" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Short post, just wanted to share a neat little discovery I made earlier today. For those of you with lots of experience with Wolfram Mathematica, this might be old hat.</p><p id="a20f" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">But for those of you who sometimes play around with functional programming with <a class="af my" href="https://www.wolframalpha.com/" rel="noopener ugc nofollow" target="_blank">Wolfram Alpha</a> or Scastie or whatever else you use to play around with functional programming, this might be a revelation.</p><p id="6408" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">In Wolfram Mathematica, there’s this concept called “<a class="af my" href="https://reference.wolfram.com/language/tutorial/PureFunctions.html" rel="noopener ugc nofollow" target="_blank">pure functions</a>.” With some caveats, you can use pure functions in Wolfram Alpha. In fact, go to Wolfram Alpha right now and type this in:</p><pre class="nx ny nz oa ob oc od oe of ay og bk"><span id="0e86" class="oh oi gu od b ij oj ok l ol om">Select[Prime[Range[100]], PrimeQ[3# + 4] &amp;]</span></pre><p id="eced" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">This is probably what you would type in if you’re curious about which prime numbers <em class="on">p</em> also give primes for 3<em class="on">p</em> + 4. For example, 5 is such a prime, since 3 × 5 + 4 = 19. By contrast, we see that 7 is not such a prime, since 3 × 7 + 4 = 25 = 5².</p><p id="e1b9" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Wolfram Alpha gives the correct response to the Wolfram Mathematica statement above: 3, 5, 11, 13, 19, and so on and so forth to 541, which just happens to be the 100th prime number.</p><p id="59fe" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">So <code class="cx oo op oq od b">Range[100]</code> just gives us the integers 1 to 100, and <code class="cx oo op oq od b">Prime[Range[100]]</code> gives us the primes indexed by the integers 1 to 100, that is, 2, 3, 5, 7, 11, 13, 17, 19, and so on to 541.</p><p id="af7f" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Then <code class="cx oo op oq od b">Select</code> tells Mathematica that we want it to select from that list the elements that return <code class="cx oo op oq od b">True</code> for the given Boolean, in this case <code class="cx oo op oq od b">PrimeQ[3# + 4] &amp;</code>.</p><p id="a28f" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">The <code class="cx oo op oq od b">#</code> “pulls in” a number from the list, multiplies it by 3 and adds 4 (you can write <code class="cx oo op oq od b">3 * # + 4</code> if you prefer). To let Mathematica know we’re invoking a pure function, we need to put <code class="cx oo op oq od b">&amp;</code> before <code class="cx oo op oq od b">Select</code>’s closing brace.</p><p id="677d" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">What if you want to iterate 3<em class="on">x</em> + 4 a few times, starting with <em class="on">x</em> = 3 and feeding the result into the next <em class="on">x</em>? In Mathematica, you can use <code class="cx oo op oq od b">NestList</code>. This will also work in Wolfram Alpha:</p><pre class="nx ny nz oa ob oc od oe of ay og bk"><span id="53c5" class="oh oi gu od b ij oj ok l ol om">NestList[3# + 4 &amp;, 3, 20]</span></pre><p id="2361" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">The <code class="cx oo op oq od b">#</code> here stands first for the initial <em class="on">x</em>, and afterwards for the previous 3<em class="on">x</em> + 4 that becomes the new <em class="on">x</em>. Again we need <code class="cx oo op oq od b">&amp;</code> to let Mathematica know we’re invoking a pure function. Then a comma and our initial argument, 3 in this case. And after that, the 20 means we want it to iterate this twenty times.</p><p id="9999" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">The result: 3, 13, 43, 133, 403, 1213, 3643, etc. These numbers get big quick, though we don’t have to worry about overflowing a 32- or 64-bit integer primitive.</p><p id="a89a" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">As you can see, some of these numbers, like 13 and 43, are prime, others are composite, like 133 = 7 × 19.</p><p id="f57e" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">This might lead us to wondering: are there prime numbers <em class="on">p</em> such that we can iterate 3<em class="on">x</em> + 4 four times and get only prime numbers?</p><p id="1eae" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">We <em class="on">could</em> create a Boolean function and use that in a <code class="cx oo op oq od b">Select</code>, something like</p><pre class="nx ny nz oa ob oc od oe of ay og bk"><span id="d0ff" class="oh oi gu od b ij oj ok l ol om">specNumberQ[n_] := (Union[PrimeQ[NestList[3# + 4 &amp;, n, 4]]] == {True});</span></pre><p id="c0c6" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">This feels inelegant. Even if we don’t save the Mathematica notebook, it seems kind of wasteful to have to name this function we might never use again.</p><p id="9d13" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">There has got to be a way to use two pure functions in one line (it’s okay if the line wraps for length), one for <code class="cx oo op oq od b">NestList</code>, the other for <code class="cx oo op oq od b">Select</code>.</p><p id="1bc9" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">I won’t bore you with a list of all the wrong things I tried. I do want to make sure you understand that this solution, which is so simple and elegant, wasn’t the first thing I tried, or even the second or third:</p><pre class="nx ny nz oa ob oc od oe of ay og bk"><span id="ed3e" class="oh oi gu od b ij oj ok l ol om">Select[Prime[Range[1000]], Union[PrimeQ[NestList[(3# + 4 &amp;), #, 4]]] == {True} &amp;]</span></pre><p id="e30d" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Note that <code class="cx oo op oq od b">3# + 4 &amp;</code> is enclosed in parentheses. That way I tell Mathematica that the scope of the pure function to be iterated is limited to <code class="cx oo op oq od b">NestList</code>’s first argument, enabling Mathematica to understand that the next <code class="cx oo op oq od b">#</code> is meant to stand for a number from <code class="cx oo op oq od b">Prime[Range[1000]]</code>.</p><p id="d58d" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">This won’t work in Wolfram Alpha, though. “Wolfram|Alpha doesn’t understand your query.” Oh well.</p><p id="d409" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Anyway, in Mathematica, this query gives only one result: 3203. We verify that 9613, 28843, 86533 and 259603 are all primes, but 778813 = 7 × 31 × 37 × 97. If we increase 1000 in the <code class="cx oo op oq od b">Range</code> to, say, 10000, we might get more numbers.</p><p id="2385" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">More importantly, however, if you ever need to use two pure functions in one line in Mathematica, now you know how: use parentheses.</p><p id="dd32" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">Actually, as it turns out, at least for this particular example, the parentheses are unnecessary. Just now I verified that</p><pre class="nx ny nz oa ob oc od oe of ay og bk"><span id="1cea" class="oh oi gu od b ij oj ok l ol om">Select[Prime[Range[1000]], Union[PrimeQ[NestList[3# + 4 &amp;, #, 4]]] == {True} &amp;]</span></pre><p id="c7a0" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">gives the correct result. With the proper placement of the ampersands, Mathematica will correctly understand where the argument for each pure function comes from.</p><p id="137f" class="pw-post-body-paragraph mz na gu nb b nc nd ne nf ng nh ni nj nk nl nm nn no np nq nr ns nt nu nv nw gn bk">I hope you get some use out of this, or at least think it might be useful to you in the future.</p></div></div></div></div></section></div></div></article></div><div class="ab cb"><div class="ci bh fz ga gb gc"><div class="or os ab iv"><div class="ot ab"><a class="ou ay am ao" href="https://medium.com/tag/programming?source=post_page-----bd892d16c411--------------------------------" rel="noopener follow"><div class="ov fj cx ow ge ox oy bf b bg z bk oz">Programming</div></a></div><div class="ot ab"><a class="ou ay am ao" href="https://medium.com/tag/wolfram-mathematica?source=post_page-----bd892d16c411--------------------------------" rel="noopener follow"><div class="ov fj cx ow ge ox oy bf b bg z bk oz">Wolfram 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For those of you with lots of experience with Wolfram Mathematica, this might be old hat.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_3":{"__typename":"Paragraph","id":"68d4c5653021_3","name":"a20f","type":"P","href":null,"layout":null,"metadata":null,"text":"But for those of you who sometimes play around with functional programming with Wolfram Alpha or Scastie or whatever else you use to play around with functional programming, this might be a revelation.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"A","start":80,"end":93,"href":"https:\u002F\u002Fwww.wolframalpha.com\u002F","anchorType":"LINK","userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_4":{"__typename":"Paragraph","id":"68d4c5653021_4","name":"6408","type":"P","href":null,"layout":null,"metadata":null,"text":"In Wolfram Mathematica, there’s this concept called “pure functions.” With some caveats, you can use pure functions in Wolfram Alpha. In fact, go to Wolfram Alpha right now and type this in:","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"A","start":53,"end":67,"href":"https:\u002F\u002Freference.wolfram.com\u002Flanguage\u002Ftutorial\u002FPureFunctions.html","anchorType":"LINK","userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_5":{"__typename":"Paragraph","id":"68d4c5653021_5","name":"0e86","type":"PRE","href":null,"layout":null,"metadata":null,"text":"Select[Prime[Range[100]], PrimeQ[3# + 4] &]","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_6":{"__typename":"Paragraph","id":"68d4c5653021_6","name":"eced","type":"P","href":null,"layout":null,"metadata":null,"text":"This is probably what you would type in if you’re curious about which prime numbers p also give primes for 3p + 4. For example, 5 is such a prime, since 3 × 5 + 4 = 19. By contrast, we see that 7 is not such a prime, since 3 × 7 + 4 = 25 = 5².","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"EM","start":84,"end":85,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":108,"end":109,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_7":{"__typename":"Paragraph","id":"68d4c5653021_7","name":"e1b9","type":"P","href":null,"layout":null,"metadata":null,"text":"Wolfram Alpha gives the correct response to the Wolfram Mathematica statement above: 3, 5, 11, 13, 19, and so on and so forth to 541, which just happens to be the 100th prime number.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_8":{"__typename":"Paragraph","id":"68d4c5653021_8","name":"59fe","type":"P","href":null,"layout":null,"metadata":null,"text":"So Range[100] just gives us the integers 1 to 100, and Prime[Range[100]] gives us the primes indexed by the integers 1 to 100, that is, 2, 3, 5, 7, 11, 13, 17, 19, and so on to 541.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":3,"end":13,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":55,"end":72,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_9":{"__typename":"Paragraph","id":"68d4c5653021_9","name":"af7f","type":"P","href":null,"layout":null,"metadata":null,"text":"Then Select tells Mathematica that we want it to select from that list the elements that return True for the given Boolean, in this case PrimeQ[3# + 4] &.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":5,"end":11,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":96,"end":100,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":137,"end":153,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_10":{"__typename":"Paragraph","id":"68d4c5653021_10","name":"a28f","type":"P","href":null,"layout":null,"metadata":null,"text":"The # “pulls in” a number from the list, multiplies it by 3 and adds 4 (you can write 3 * # + 4 if you prefer). To let Mathematica know we’re invoking a pure function, we need to put & before Select’s closing brace.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":4,"end":5,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":86,"end":95,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":183,"end":184,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":192,"end":198,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_11":{"__typename":"Paragraph","id":"68d4c5653021_11","name":"677d","type":"P","href":null,"layout":null,"metadata":null,"text":"What if you want to iterate 3x + 4 a few times, starting with x = 3 and feeding the result into the next x? In Mathematica, you can use NestList. This will also work in Wolfram Alpha:","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":136,"end":144,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":29,"end":30,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":62,"end":63,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":105,"end":106,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_12":{"__typename":"Paragraph","id":"68d4c5653021_12","name":"53c5","type":"PRE","href":null,"layout":null,"metadata":null,"text":"NestList[3# + 4 &, 3, 20]","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_13":{"__typename":"Paragraph","id":"68d4c5653021_13","name":"2361","type":"P","href":null,"layout":null,"metadata":null,"text":"The # here stands first for the initial x, and afterwards for the previous 3x + 4 that becomes the new x. Again we need & to let Mathematica know we’re invoking a pure function. Then a comma and our initial argument, 3 in this case. And after that, the 20 means we want it to iterate this twenty times.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":4,"end":5,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":120,"end":121,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":40,"end":41,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":76,"end":77,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":103,"end":104,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_14":{"__typename":"Paragraph","id":"68d4c5653021_14","name":"9999","type":"P","href":null,"layout":null,"metadata":null,"text":"The result: 3, 13, 43, 133, 403, 1213, 3643, etc. These numbers get big quick, though we don’t have to worry about overflowing a 32- or 64-bit integer primitive.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_15":{"__typename":"Paragraph","id":"68d4c5653021_15","name":"a89a","type":"P","href":null,"layout":null,"metadata":null,"text":"As you can see, some of these numbers, like 13 and 43, are prime, others are composite, like 133 = 7 × 19.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_16":{"__typename":"Paragraph","id":"68d4c5653021_16","name":"f57e","type":"P","href":null,"layout":null,"metadata":null,"text":"This might lead us to wondering: are there prime numbers p such that we can iterate 3x + 4 four times and get only prime numbers?","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"EM","start":57,"end":58,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":85,"end":86,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_17":{"__typename":"Paragraph","id":"68d4c5653021_17","name":"1eae","type":"P","href":null,"layout":null,"metadata":null,"text":"We could create a Boolean function and use that in a Select, something like","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":53,"end":59,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"EM","start":3,"end":8,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_18":{"__typename":"Paragraph","id":"68d4c5653021_18","name":"d0ff","type":"PRE","href":null,"layout":null,"metadata":null,"text":"specNumberQ[n_] := (Union[PrimeQ[NestList[3# + 4 &, n, 4]]] == {True});","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_19":{"__typename":"Paragraph","id":"68d4c5653021_19","name":"c0c6","type":"P","href":null,"layout":null,"metadata":null,"text":"This feels inelegant. Even if we don’t save the Mathematica notebook, it seems kind of wasteful to have to name this function we might never use again.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_20":{"__typename":"Paragraph","id":"68d4c5653021_20","name":"9d13","type":"P","href":null,"layout":null,"metadata":null,"text":"There has got to be a way to use two pure functions in one line (it’s okay if the line wraps for length), one for NestList, the other for Select.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":114,"end":122,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":138,"end":144,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_21":{"__typename":"Paragraph","id":"68d4c5653021_21","name":"1bc9","type":"P","href":null,"layout":null,"metadata":null,"text":"I won’t bore you with a list of all the wrong things I tried. I do want to make sure you understand that this solution, which is so simple and elegant, wasn’t the first thing I tried, or even the second or third:","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_22":{"__typename":"Paragraph","id":"68d4c5653021_22","name":"ed3e","type":"PRE","href":null,"layout":null,"metadata":null,"text":"Select[Prime[Range[1000]], Union[PrimeQ[NestList[(3# + 4 &), #, 4]]] == {True} &]","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_23":{"__typename":"Paragraph","id":"68d4c5653021_23","name":"e30d","type":"P","href":null,"layout":null,"metadata":null,"text":"Note that 3# + 4 & is enclosed in parentheses. That way I tell Mathematica that the scope of the pure function to be iterated is limited to NestList’s first argument, enabling Mathematica to understand that the next # is meant to stand for a number from Prime[Range[1000]].","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":10,"end":18,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":140,"end":148,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":216,"end":217,"href":null,"anchorType":null,"userId":null,"linkMetadata":null},{"__typename":"Markup","type":"CODE","start":254,"end":272,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_24":{"__typename":"Paragraph","id":"68d4c5653021_24","name":"d58d","type":"P","href":null,"layout":null,"metadata":null,"text":"This won’t work in Wolfram Alpha, though. “Wolfram|Alpha doesn’t understand your query.” Oh well.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_25":{"__typename":"Paragraph","id":"68d4c5653021_25","name":"d409","type":"P","href":null,"layout":null,"metadata":null,"text":"Anyway, in Mathematica, this query gives only one result: 3203. We verify that 9613, 28843, 86533 and 259603 are all primes, but 778813 = 7 × 31 × 37 × 97. If we increase 1000 in the Range to, say, 10000, we might get more numbers.","hasDropCap":null,"dropCapImage":null,"markups":[{"__typename":"Markup","type":"CODE","start":183,"end":188,"href":null,"anchorType":null,"userId":null,"linkMetadata":null}],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_26":{"__typename":"Paragraph","id":"68d4c5653021_26","name":"2385","type":"P","href":null,"layout":null,"metadata":null,"text":"More importantly, however, if you ever need to use two pure functions in one line in Mathematica, now you know how: use parentheses.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_27":{"__typename":"Paragraph","id":"68d4c5653021_27","name":"dd32","type":"P","href":null,"layout":null,"metadata":null,"text":"Actually, as it turns out, at least for this particular example, the parentheses are unnecessary. Just now I verified that","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_28":{"__typename":"Paragraph","id":"68d4c5653021_28","name":"1cea","type":"PRE","href":null,"layout":null,"metadata":null,"text":"Select[Prime[Range[1000]], Union[PrimeQ[NestList[3# + 4 &, #, 4]]] == {True} &]","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_29":{"__typename":"Paragraph","id":"68d4c5653021_29","name":"c7a0","type":"P","href":null,"layout":null,"metadata":null,"text":"gives the correct result. With the proper placement of the ampersands, Mathematica will correctly understand where the argument for each pure function comes from.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"Paragraph:68d4c5653021_30":{"__typename":"Paragraph","id":"68d4c5653021_30","name":"137f","type":"P","href":null,"layout":null,"metadata":null,"text":"I hope you get some use out of this, or at least think it might be useful to you in the future.","hasDropCap":null,"dropCapImage":null,"markups":[],"codeBlockMetadata":null,"iframe":null,"mixtapeMetadata":null},"PostViewerEdge:postId:bd892d16c411-viewerId:lo_aa2d210293ba":{"__typename":"PostViewerEdge","shouldIndexPostForExternalSearch":true,"id":"postId:bd892d16c411-viewerId:lo_aa2d210293ba"},"Tag:programming":{"__typename":"Tag","id":"programming","displayTitle":"Programming","normalizedTagSlug":"programming"},"Tag:wolfram-mathematica":{"__typename":"Tag","id":"wolfram-mathematica","displayTitle":"Wolfram Mathematica","normalizedTagSlug":"wolfram-mathematica"},"Tag:wolfram-language":{"__typename":"Tag","id":"wolfram-language","displayTitle":"Wolfram Language","normalizedTagSlug":"wolfram-language"},"Tag:functional-programming":{"__typename":"Tag","id":"functional-programming","displayTitle":"Functional Programming","normalizedTagSlug":"functional-programming"},"Tag:pure-function":{"__typename":"Tag","id":"pure-function","displayTitle":"Pure Function","normalizedTagSlug":"pure-function"},"Post:bd892d16c411":{"__typename":"Post","id":"bd892d16c411","collection":null,"content({\"postMeteringOptions\":{}})":{"__typename":"PostContent","isLockedPreviewOnly":false,"bodyModel":{"__typename":"RichText","sections":[{"__typename":"Section","name":"b9eb","startIndex":0,"textLayout":null,"imageLayout":null,"backgroundImage":null,"videoLayout":null,"backgroundVideo":null}],"paragraphs":[{"__ref":"Paragraph:68d4c5653021_0"},{"__ref":"Paragraph:68d4c5653021_1"},{"__ref":"Paragraph:68d4c5653021_2"},{"__ref":"Paragraph:68d4c5653021_3"},{"__ref":"Paragraph:68d4c5653021_4"},{"__ref":"Paragraph:68d4c5653021_5"},{"__ref":"Paragraph:68d4c5653021_6"},{"__ref":"Paragraph:68d4c5653021_7"},{"__ref":"Paragraph:68d4c5653021_8"},{"__ref":"Paragraph:68d4c5653021_9"},{"__ref":"Paragraph:68d4c5653021_10"},{"__ref":"Paragraph:68d4c5653021_11"},{"__ref":"Paragraph:68d4c5653021_12"},{"__ref":"Paragraph:68d4c5653021_13"},{"__ref":"Paragraph:68d4c5653021_14"},{"__ref":"Paragraph:68d4c5653021_15"},{"__ref":"Paragraph:68d4c5653021_16"},{"__ref":"Paragraph:68d4c5653021_17"},{"__ref":"Paragraph:68d4c5653021_18"},{"__ref":"Paragraph:68d4c5653021_19"},{"__ref":"Paragraph:68d4c5653021_20"},{"__ref":"Paragraph:68d4c5653021_21"},{"__ref":"Paragraph:68d4c5653021_22"},{"__ref":"Paragraph:68d4c5653021_23"},{"__ref":"Paragraph:68d4c5653021_24"},{"__ref":"Paragraph:68d4c5653021_25"},{"__ref":"Paragraph:68d4c5653021_26"},{"__ref":"Paragraph:68d4c5653021_27"},{"__ref":"Paragraph:68d4c5653021_28"},{"__ref":"Paragraph:68d4c5653021_29"},{"__ref":"Paragraph:68d4c5653021_30"}]},"validatedShareKey":"","shareKeyCreator":null},"creator":{"__ref":"User:cccc8c3341e1"},"inResponseToEntityType":null,"isLocked":false,"isMarkedPaywallOnly":false,"lockedSource":"LOCKED_POST_SOURCE_NONE","mediumUrl":"https:\u002F\u002Falonso-delarte.medium.com\u002Fin-wolfram-mathematica-you-can-have-two-pure-functions-on-one-line-bd892d16c411","primaryTopic":null,"topics":[{"__typename":"Topic","slug":"programming"}],"isPublished":true,"latestPublishedVersion":"68d4c5653021","visibility":"PUBLIC","postResponses":{"__typename":"PostResponses","count":0},"clapCount":63,"allowResponses":true,"isLimitedState":false,"title":"In Wolfram Mathematica, you can have two pure functions on one line","isSeries":false,"sequence":null,"uniqueSlug":"in-wolfram-mathematica-you-can-have-two-pure-functions-on-one-line-bd892d16c411","socialTitle":"","socialDek":"","canonicalUrl":"","metaDescription":"","latestPublishedAt":1545678645462,"readingTime":3.3735849056603775,"previewContent":{"__typename":"PreviewContent","subtitle":"Short post, just wanted to share a neat little discovery I made earlier today. 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