were i to divide my average day into percentage, it would most resemble the following:

25%: sleep

10%: studying my reflection in the mirror

15%: talking to my homo friends about being gay and neighboring hot men

15%: “i’m on leave from MIT, yes. how many shots in your cappuccino would you like?”

7%: masturbation

6%: studying for/attending analysis and algebra

10%: reading 10 men, vogue, the new yorker, GRE prep books, the times crossword, making anagrams of random words and products of two-digit numbers i see on public transport

i would imagine the other eighth of my time is me staring into space, or standing in a secluded corner to pull underwear out of my butt or pick my nose.

my life is good, but the move back to boston will be fivefold more entertaining; i miss having conversations with groups of friends who are not all gay.

oh. my summer, you ask?

party after party after party…it’s quite the life.

the first i attended was in the middle of june: gary foster’s at the W hotel in the entertainment district. the party started at seven. having arrived at eight o’clock, i was surprised to find myself in the company of only a dozen men. an hour later, this number multiplied fivefold and by ten, the room was swarming with cliques of gay men exchanging catty glances and friendly assgrabs.

upon arrival i met the bartender, a pale woman in her mid-thirties who followed the question of where i attended school with “so what’s your IQ?”. she stood next to a fellow named marc anthony, with whom i spent between eight and nine smoking the last bit of pot i had in my wallet with two knives over the stove in his town house. for the remainder of the night, he spent clearing his throat and i spent thinking how it was that he had named his dog morroco and how when talking to gary about an upcoming trip that evening, marc did not know the locations of fez or marrakesh.

i ducked away for a while and while enjoying a gin & tonic (amazing, i can drink them again after countless nights of 21-ounce bombay mashes in towers, no?), a group of guys my age gave me the look and the tallest and most attractive one bearing a striking resemblance to gabriel cira complimented me on my polka-dot shirt. “i got it at barney’s.” his eyes grew even fuller and he smirked approvingly. we ran into each other again at john’s fourth-of-july party and again yesterday at chris’s big birthday bash yesterday.

while the pool area and above deck were rented, nobody stood in shorts (save for two very drunk men making out in the pool four hours into the party).  by eleven, i was in line for the bathroom facetiously playing a sycophant to a tweezed and tanned adonis named shelton in an attempt to win over a laugh. shortly thereafter i ended up in a car with two of his friends. we were headed for the bars. while driving from the entertainment district to homoville, booze-fueled railings were tossed around in a slapdash and characteristically gay fashion.

moments later, the driver was punched in the side of the head by the meathead in the passenger’s seat. the car stopped immediately and in turning to the side to demand that everyone leave the car, blood started to drip from his brow. we got out. shelton and i caught a cab home.

and since then i’ve been known as the guy in the marc jacobs shirt who goes to MIT and ended up in that car with those three musclequeens.

he imed me. and told me he got a boyfriend. something he never admitted of our six-month relationship.

in other news, i started special orthogonal groups in the 18.701/2 book.

we’re together. and everything is perfect because you’re there. i lead the queen and you play the ace. i toss a two and you play a three to his losing nine. together, we play infallibly. every card you and i throw is effortless because, without a doubt, we both know which cards we will play.

the game ends and we win with nine bags. 

the sun shines brightly just like our pairing smiles.

and everyone is giggling boisterously.

sometimes i like to close my eyes and pretend that i’m fabulous and popular ‘cuz i make awesome clothes

red, blue, green, or translucent pink? the choices of solo cups at n.’s birthday were endless and were it not for the racing green i had never before seen, i probably would have never changed my mind. my eyes traced the titles behind the drink table and i hastily judged the stodgy books i had not read since high school. only remembering from the invisible man the ceiling with 1369 (37 to the power of 2) lights and the tomato soup made from ketchup packets and hot water, i flipped through the first several pages hoping to find the references. the music stopped playing and n. stood across the room booing, releasing a chain of similar utterances of disapproval. i opted for an “oh no she DIDn’t” and when the guy closest to me turned in my direction to express his confusion, i crossed my eyes, stuck out my tongue, and walked away.

there were several attractive men last night (of course with none of whom i could hold a conversation without a two- or three-second pause that allowed them just enough time to make the precipitate decision to excuse themselves). my inability to hold people’s attention for more than the duration of six seconds just baffles me. knowing that the only other new people that would hold polite conversation were straight women, i made a beeline for the woman at the keg. d. was scrappy. her voice was coarse and left cheek was covered by a band-aid. she wore a trucker hat. “you are the first person to ask me that tonight”, she answered in response to my question about the bandaid. “i’m usually good at not picking at my zits, but this time, i just couldn’t help myself.” she paused for a moment to look far off into space, perhaps back to the moment when she ultimately decided that it was a good idea to pop her pus-filled blemish. we continued to briefly exchange our life stories and i found out that we lived about twenty-five blocks away in manhattan last year. “did you ever go to suite on 107th and amsterdam?” she couldn’t quite remember where it was and pulling her boyfriend away from his friends, she asked him if they had been and he, too, had trouble remembering. i tried to remind her of the noteworthy qualities of the place: small, dark, gay. “GAY”, she exclaimed. “i was going to ask you if it was gay or not.” she remembered and we all shared approval for its weekly drag performances. she excused herself to smoke marijuana and i eyed the food table.

another fantastic feature of the birthday party had to be the collations: chicken wings, gummi bears, and pretzel sticks. i munched and tried to look suggestively jejune as possible while eating an orange wedge. successfully, three glances fell in my direction and i hammed it up by biting my bottom lip. n. bopped his way through the sea of bears in elastic suspenders and we found ourselves separated by the couches. we excitedly look at each other and winded our way through the furniture in a manner that was humorously vaudeville. we danced. it was his birthday. he was excited. i was excited. it was his birthday!

later i found myself on the roof in mixed company. m. wanted a cigarette, so we picked a group and interjected. there was a cute guy in a trucker hat. it said something like “scrunchy” or “scratchy” and i am pretty sure that i will forever remember him as ” that cute scrunchy guy.” i couldn’t tell you the names of the other three gentleman in the group that i had formally met, but they seemed alright. m. got her cigarette and when it was her turn to make conversation, she asked the cigarette guy how old he was and then the conversation devolved from “i’m twenty-five.” to “oh, you’re twenty-one — good for you.” they disbanded, some to go downstairs and the others to move five feet away from us to continue their discussion. 

it was cold until katherine came out. she looked as beautiful as ever. her wavy brown her moved in the wind and i took another moment to admire her outfit. ms. grey was back in town and informing the fashion-savvy that indeed grey was the new grey. we were goofy and took pictures. it was fun.

i was mildly disappointed that despite that fifty million bears there, i did not strike anyone’s fancy, but the party was good. a few games of connect four, the man in the rubber shirt, and one very sweaty and happy n. wrapped up what was all-in-all a good night.

i dreamt about a retreat to the bucolic flatlands of texas. we arrived at our destination to find what looked to be an old cavalry, temporarily renovated for our school’s needs. most of the space was shaded by corrugated aluminum and the remainder was set aside for two pools,  one of which was fenced off. designated to a new position, it was my job to help grill for lunchtime. i carried charcoal briquets back to my station through the back corridor. the straw-covered mud and the balmy air reminded me of the cattle display at the state fair. dozens of burgers later, my shift ended and in walking to the western side of the pavillion, i came across a sign that read: “12:30 Commencement Speech, Marcus Gonzales-DeCardenas and President Barack Obama.”

i missed it. clearly the alimentary welfare of my classmates was more important than the chance to meet and speak with obama. i turned around and there he was, this man whom i had never seen before, exceedingly handsome with a bright smile and a pistachio collared shirt. a moment later, he walked away and i continued to walk down the pavillion. towards the pools, midways of squirt-gun races, ring tosses, and shooting games were lined with hunched students, fixed on their stuffed animal prizes and there again, i could feel the state fair — but even closer than before. the cloying smell of cotton candy and merriment of drunk middle-aged men guffawing over the world’s fattest alligator were the only things missing.

the private pool wasn’t completely enclosed; there were missing boards through which one could easily see the ongoings of the putative elite. there were many swimming, but my eye only caught two specifically: the man of my deluded dreams and her, the annoying slutface who — for the past several weeks — has entered my life with no other intention but to shit on my parade. what was it supposed to mean? i could think of explanations, but none of which would be particuarly enlightening, much less fun to discuss.

i turned around and there he was, the gorgeous  gentleman, floating on an inflatable donut with his chest hair perfectly-trimmed and sculpted and flawless grey eyes, his smile still as charming as ever.  i took two steps towards him and he swam towards me and then, i woke up.

Dickson conjectured in 1904 that given a family of linear functions with integer coefficients a_i > 1 and b_i:

a₁n + b₁, a₂n + b₂, a_kn + b_k,

then there are infinitely many integers n > 0 for which these are simultaneously prime unless they “obviously cannot be” (that is, unless there is a prime p which divides the product of these for all n). This is now called Dickson’s Conjecture.Many conjectures follow from Dickson’s conjecture. For example, if the functions are n and n+2, then Dickson’s conjecture implies the twin prime conjecture. If the functions are n and 2n+1, then we have the conjecture that there are infinitely many Sophie Germain primes. The prime k-tuple conjecture is also a special case of Dickson’s conjecture, as is the conjecture that for each positive integer n, there is an arithmetic sequence of n primes. Finally, if Dickson’s conjecture is true, then there are infinitely many composites, Mersenne numbers, as well as infinitely many Carmichael numbers with just three prime factors.

Schinzel and Sierpinski extended Dickson’s conjecture into the analogous Hypothesis H for integer polynomials with arbitrary degree.

Dickson’s conjecture can be heuristically quantified as follows. Let w(p) be the number of solutions to

(a₁n + b₁)(a₂n + b₂)^.…^.( a_kn + b_k) = 0 (mod p).

Then the expected number of positive integers n less than N which yield k simultaneous primes

a₁n + b₁, a₂n + b₂, a_kn + b_k,

is conjectured to be asymptotic to

: (

where the products are taken over the set of all primes p.If we replace “there are infinitely many integers n > 0 for which these are simultaneously prime” in Dickson’s conjecture with “there is an integern > 0 for which these are simultaneously prime,” then we appear to weaken the conjecture. But it is easy to show these two conjectures are equivalent!

Another important conjecture that follows from Dickson’s conjecture is that if a₁ < a₂ < … < a_k are nonzero integers for which there is no prime dividing the product

(x + a₁)(x + a₂)^.…^.(x + a_k)

for all integers n, then there are infinitely many positive integers n for which

x+a₁, x+a₂, . . . x+a_k,

are consecutive primes.This form of Dickson’s conjecture implies that for each positive integer n, there are infinitely many arithmetic sequence of n consecutive primes. It also implies Polignac’s conjecture, and …

valentine’s day valentines’svalentinesvalentieangavanvalvavavvalentienensvalentienes

WITH SWEETHEARTS deformed in the shape of goldfish, girls /raving/ over “the largest ugg store in the world”, my love don’t cost a thing at neiman marcus, sassy conversation with thuy in the shoe department at barney’s, one hundred dollar-whipped cream crackers, the women in ysl nasally raving “oh my gggoooddd, you look fabulous”, free coffee, rhinestone-bedizened muumuus, and that really cute guy from the party last night

BREAKDOWNANDLETITALLLOOOOUUUTTTT

several days ago, i came to the unpleasant conclusion that i would in fact be spending saturday alone. for a brief moment i thought that this year would be different from the previous four. at sixteen that day, i had to be awake at four-thirty to meet for an academic competition. for the first time in two years, it snowed. reasoning that i would be more tired had i slept for two hours instead of not sleeping at all, i stayed up all night. chris called me and we talked for several hours. plesantries were exchanged. i told him about how excited i was about the snow and he told me how excited he was to talk to me. i thought about how much i wanted my hands in his blond hair and my dark brown eyes fixed on the blue in his.

a few hours later i was on a bus to the middle of nowhere. i wore a pink shirt and pinstripe slacks from the gap. i sat against the window, listening to the flaming lips and trying to read the brothers karamazov in the dark. the first competition was number sense at eight fifty. at eight forty-nine i was staring at my named printed on the unopened number sense test. i considered the possible problems and reminded myself to make my answers legible (any mark other than the answer written in the blanks would result in an automatic wrong answer). i guess scratchwork is the mathematical dilettante’s quintessential fault. i looked up. there was everyone else: thirty-nine other high school students, eagerly awaiting the start time, eyes exhausted, hair and outfits distraught, seething frustration and anxiety.

the test started. the sound of scratching pens filled the room, disrupted four minutes later by me, the first to flip the sheet over in order to answer the remaining forty-five questions. sheets began to flip slowly over the next six minutes. time was called at nine and everyone left the room. because number sense was the only competition i did for fun, i can’t say that i remember anything else about the day other than the delicate snow that fell on our way back to dallas and the trophies from the competition that i would throw in the trash shortly after getting home.