{"id":124589,"date":"2018-04-25T09:00:11","date_gmt":"2018-04-25T13:00:11","guid":{"rendered":"https:\/\/www.theparisreview.org\/blog\/?p=124589"},"modified":"2018-04-25T13:29:06","modified_gmt":"2018-04-25T17:29:06","slug":"prime-numbers","status":"publish","type":"post","link":"https:\/\/www.theparisreview.org\/blog\/2018\/04\/25\/prime-numbers\/","title":{"rendered":"Prime Numbers"},"content":{"rendered":"

\"\"<\/a><\/p>\n

 <\/p>\n

I suppose there are mathematicians out there \u201cworking on prime numbers.\u201d I don\u2019t know if there are. There probably are. They\u2019re putting on coffee at\u00a011 o\u2019clock<\/span><\/span>\u00a0at night. They\u2019re getting upset at each other on email, cussing. Or adopting \u201cwithering tones.\u201d They\u2019re working.<\/p>\n

I myself don\u2019t work on prime numbers. I work \u2026 on working on prime numbers. Not really. I\u2019ve given the matter some thought. I\u00a0did<\/i>\u00a0work on prime numbers for a few ecstatic days in the year 1999. That was the outcome of more than 10 years of brooding. Intermittent brooding. And now it\u2019s been almost 20 years since\u00a0that<\/i>. And now I brood over people who brood about prime numbers. I understand them.\u00a0<\/p>\n

I don\u2019t want to explain prime numbers, but I\u2019d better. Let\u2019s at least mix it up. I\u2019ll define prime numbers the way a child does\u2014the way a child\u00a0has<\/i>\u00a0to. Prime numbers are those where, if you had a mass of pencils of that number, you wouldn\u2019t be able to separate the pencils into evenly distributed piles. Like if you have 7 pencils. Try to separate \u2019em into nice even piles.\u00a0(One pencil is not a pile, okay?)<\/p>\n

 <\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Ah! doesn\u2019t work! \u2014Prime number.\u2014<\/p>\n

I know you know what a prime number is. But there\u2019s a strange pleasure in explaining things like that, over and over. And the existence of that pleasure is meaningful. We\u2019ll come back to it another day.<\/p>\n

Once upon a time, I was in college. I had an engineering-major roommate. I loved him, though he was an asshole. As was I. He loved me too. But to get back to my story. He knew all about math and programming and was also a visionary. I was a visionary. We had visions.<\/p>\n

Put a straw in a soda. Cover the end with your finger. Take the straw out, the soda stays in the straw. Take your finger off, out comes the soda. So why can\u2019t we make an\u00a0inverted swimming pool\u2014up into which\u00a0you would leap\u2014on the same principle? And so on.<\/p>\n

I liked to set him teasers. One day it was prime numbers. Look: there\u2019s no space at all between prime numbers 2 and 3. That\u2019s the last time\u00a0that<\/i>\u00a0happens! Between 3 and 5 there\u2019s a \u201cspace\u201d: the 4. Between 5 and 7 there\u2019s a space. But between 7 and 11, uh-oh! T<\/em>hree<\/i>\u00a0spaces. Okay. So the question is: How far up the number line do you have to go to encounter 101 \u201cspaces\u201d between 2 prime numbers?<\/p>\n

We tried to guess. He had a guess; I didn\u2019t have a guess. He flashed on some kind of equation that would answer the question in no time. Except it didn\u2019t work. Memory says he covered both sides of 2 pieces of paper with Einstein before his hypothesis was pronounced dead. All this, in 1987. Itself a prime number.<\/p>\n

Now skip to also-prime 1999. Brooklyn. Lot of time on my hands. I resolved on getting to the bottom of the matter by brute force. Took a big piece of paper. Wrote out the first 1,000 numbers. I didn\u2019t have a computer. I took a magic marker, crossed out all the numbers divisible by 2. Then by 3. Then by 5. This system has a name: sieve of Eratosthenes. I\u2019m surprised it has a name; it\u2019s a pretty obvious procedure. Here is a picture of Eratosthenes\u2019s cryogenically preserved head:<\/p>\n

 <\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

I wasn\u2019t really hoping to find that 101-item gap. I just wanted to see what patterns would arise. I was hoping to put myself in a position to venture a guess as to where, more or less, my unicorn was hiding.<\/p>\n

You see where this is going. There was no bloody pattern. I did the whole thing over, starting with 2 poster-size pieces of paper and a fistful of colored markers. Sieved out all the primes up to 5,000<\/i>. The largest gap I found was 33 \u201cspaces\u201d between the prime numbers 1,327 and 1,361.<\/p>\n

The following picture cost me blood\u2014so look at it.<\/p>\n

 <\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

Most of the nonprimes there are divisible by 2, 3, 5, or 7; I have annotated the more exotic cases of nonprimeness, my favorite being 1,333\u201431 piles of 43 pencils each. Or, if you like, 43 piles of 31 pencils each.<\/p>\n

You should be alarmed, though. That 33-space gap did not occur in the 4,000\u20135,000 range. Far from. I don\u2019t even\u00a0know<\/i>\u00a0when the next one occurs. I\u2019d have to go through that sieve nightmare again. Except I wouldn\u2019t, \u2019cuz there are computers now.<\/p>\n

So where would\u00a0you<\/i>\u00a0guess the first 101-space gap occurs? Don\u2019t bother guessing. I\u2019ll just tell you. There are computers now.<\/p>\n

It occurs between the prime numbers\u00a01,444,309<\/b>\u00a0and\u00a01,444,411<\/b>.<\/p>\n

Between the numbers 2 and 2,000,000, there are precisely 3 such 101-space chains. And there are 34 of \u2019em in all if you go to 10,000,000.<\/p>\n

Now it has always seemed to me that such gaps must become more and more common if you simply pursue the number line into outer space. Somewhere way, way out there, there must be cases of gaps, not of 101 composite numbers but of 1,000,000,001. There must even be cases where prime numbers a mile long are posted, slowly rotating in inspissated gloom, 1,000,000,001<\/em>\u00a0nonprime numbers on either side<\/i>.<\/p>\n

Supreme loneliness. Silence. The darkness of the outer reaches. And no way to get a message to them.<\/p>\n

 <\/p>\n

Anthony Madrid lives in Victoria, Texas. His second book is\u00a0<\/em>Try Never<\/a>. He is a correspondent for the\u00a0<\/em>Daily.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

  I suppose there are mathematicians out there \u201cworking on prime numbers.\u201d I don\u2019t know if there are. There probably are. They\u2019re putting on coffee at\u00a011 o\u2019clock\u00a0at night. They\u2019re getting upset at each other on email, cussing. Or adopting \u201cwithering tones.\u201d They\u2019re working. I myself don\u2019t work on prime numbers. I work \u2026 on working […]<\/p>\n","protected":false},"author":1005,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[419],"tags":[22908,15238,11973,7210,22190],"class_list":["post-124589","post","type-post","status-publish","format-standard","hentry","category-arts-culture","tag-anthony-madrid","tag-einstein","tag-eratosthenes","tag-pencils","tag-prime-numbers"],"acf":[],"yoast_head":"\nPrime Numbers by Anthony Madrid<\/title>\n<meta name=\"description\" content=\"Our poetry correspondent, Anthony Madrid, takes up prime numbers.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.theparisreview.org\/blog\/2018\/04\/25\/prime-numbers\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Prime Numbers by Anthony Madrid\" \/>\n<meta property=\"og:description\" content=\"April 25, 2018 \u2013   I suppose there are mathematicians out there \u201cworking on prime numbers.\u201d I don\u2019t know if there are. 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