n – n2 + 41 is prime for all values of n for 0 to 40.
n – n2 + 41 is prime for all values of n for 0 to 40.
There is nothing so exotic as the mundane… and nothing so mundane as the exotic…..
The Cult of Infinite Hermaphrodites
When neophytes enter the Cult of Infinite Hermaphrodites at Xidar, they are taught, amidst their initial duties of sweeping and service, the operations of simple arithmetic. Then, at the end of their first year, now most practised in this arithmetic, they are asked to say which number it is that, self-mated, beareth 4. And they reply, of course, that 4 is born of self-mated 2. And asked the same of 9, they reply 3; and of 16, they reply 4. Thus it is (they now learn) that 2 is called by the Cult the hermaphrodite of 4, as 3 is the hermaphrodite of 9, and 4 of 16. Then the neophytes are asked to say which number it is that, self-mated, beareth 1: which is to say, what is the hermaphrodite of 1? And they reply, of course, that 1 is auto-hermaphroditic, self-mating to bear itself. And then, in mildest, most deceptive tones, they are asked to name the hermaphrodite of 2. And here, in this simplest of questions, they stand (tho’ they know it not) on the brink of a Mysterium Magnissimum et Tremendissimum, a Riddle Most Mighty and Awesome.
Now, ’tis evident that the hermaphrodite of 2 falleth betwixt 1 and 2, for 1 is the Auto-Hermaphrodite, self-mating to bear itself, and self-mated 2 beareth 4, as remarked above. But where-betwixt doth the requested hermaphrodite fall? The neophytes know not. So they are told: test the mid of 1 and 2, which is 1½, or 3/2. Self-mated, this bears 9/4, or 2¼. And this falls too high. So, subtract a ½ of a ½ from 1½, for 1¼, or 5/4. Self-mated, this bears 25/16, or 1 and 9/16. And this falls too low. So, add a ½ of a ¼ to 1¼, for 1⅜, or 11/8. Self-mated, this bears 121/64, or 1 and 57/64. Again, too low. So, add a ½ of an ⅛ to 1⅜, for 23/16, or 1 and 7/16. Self-mated, this bears 529/256, or 2 and 17/256. Too high. And thus the neophytes proceed for a day, dividing and subtracting, dividing and adding, ever approximating the hermaphrodite of 2.
But do they ever reach it? Could they ever reach it, by this or any other mode of rational approximation? And here is the Mighty Mystery, the Riddle that Wrencheth the Brain, for the Cult replieth: Nay, Nay, Never! For It hath an incontrovertible proof that demonstrateth, by easy steps of simple logic, that the hermaphrodite of 2 is impossibly a ratio of finite integer to finite integer: which is to say, it must be infinite. Were the sky all parchment, the seas all ink, and gulls all plucked for quills, the hermaphrodite of 2 remained irrecordable. And more than this: the Cult can prove, by adaptation of the aforementioned logic, that the hermaphrodites of all integers, save the perfect squares, are similarly infinite and irrecordable, eternally elusive of finite man, yet definable even in their boundless nature by his skull-boxed brain-speck. And this truth the Cult flaunteth to the profane in its very name, which titillateth and tempteth, yet yieldeth not the guessed-at, the hoped-for fruit.
All hail, O World, the lowly Worm,
Which, same to same, exchangeth sperm!
And twines its twin, beneath the moon,
To grant itself renewal’s boon!
Next bow, yea bow, and loudly hail
The spiral-foot, the crawling Snail!
That twines its twin, ’midst nuptial slime,
To slay the slayer, scything Time!
From The Hymn to Hermaphroditi.
Our Lady of the Gutter
Walking on the shaded side of Longsands Avenue, he saw a small lady’s-mantle in the gutter. Alchemilla mollis. The soft little alchemical one. It was new-grown and its pleated leaves were fresh and green against the cement. He wished he could spin a poem out of it, out of the unexpected sight, something deep and mysterious and Larkinesque. A line, or two lines, occurred to him. The line of the gutter/Stutters with green. But where to go after that? Later, walking back along Longsands Road, he heard a twittering, or thought he did, and looked up to see swifts high up, swirling, swooping, seeking insects he couldn’t see. Aëroplankton. Again he wished he could capture the moment, condense the sight into potent language. He thought a little. Sickle-wing swifts/Reap the insected air. But again, where to go after that? He liked “insected air”, though. It had an assonance of “infected air”. But why not a portmanteau? Reap the insfected air. He’d always liked words that started with sph and sf. Sphinx. Sphragistics. Sfumato. Sforzando. “Insfected air” would be air that had insects and pollution in it. Reaped by sickle-wing swifts, fluttering their wings like eyelashes. He remembered that Ted Hughes had written a poem about swifts, but he didn’t like it. It had reminded him of Gerard Manley Hopkins, left out in the rain for a week or two. Perhaps Larkin had written about swifts too, or mentioned them. He hadn’t finished The Complete Poems yet.
Later in the day, he was walking along the promenade. The tide was out, but a tongue of water had been left at the foot of the gold-lichen-splashed sea-wall. He climbed down the steps to it, squatting on his haunches and looking into the wind-rippled water. He saw a shrimp first, then, perhaps when the shock of his shadow or the tremors of his arrival had subsided, tiny flounder began to flick to and fro over the sandy mud. When you saw them move and settle, you could just see their outlines. Otherwise it would be impossible to know where they were. The previous year, on a very hot day, another flounder had been defeated by its camouflage: not protected by it, but doomed. The same tongue of water had stretched along the foot of the sea-wall, but it had been shrinking in the fierce sun. He had rescued some of the dozens of shrimp that crowded the damp but drying sand at one end of the tongue. They were flicking themselves into the air as they dried, hoping to land in water, disappointed again and again. He collected them on his palm and threw them into the deeper water in the middle of the tongue.
As always when he did something like that, he wondered whether it was better not to interfere. Perhaps preserving the weak just means greater misery in future. But they weren’t weak, they were unlucky. Probably. But perhaps unluckiness was weakness too. Because weakness led to unluckiness. Then he left the sand and the shrimps to walk to Merrimont Park. Later, walking back along the promenade, he walked down the steps again and looked at the sand where he had rescued the shrimps. It was completely dry now and he saw what he hadn’t seen before: a tiny dead flounder. If he had seen it before, he would have rescued it, but its camouflage had been too good, defeating his eye, so it had dried and died with dozens of shrimp, hundreds of them, thousands. A hammic hecatomb. Unnoticed and unmourned, except by him. Nature was always sacrificing her self to herself. Insects, arthropods, myriad little lives lost daily, hourly. Presided by whom? Perhaps Our Lady of the Gutter. Nostra Signora della Cunetta. Nuestra Señora de la Cuneta. Our Lady of the Overlooked and Interstitial. He wished he could write a poem about her, complete the poems he had begun about the lady’s mantle and the swifts, but perhaps it was better that he couldn’t. Prose was better for stumbling, for incompleteness, for the rhythmless and rhymeless way the world threw fragments of beauty and consolation at you.