Mersenne’s Mistake

by Jason Earls

part 1 of 2


A single candle glowed in the cell of the monastery, its yellow rays reflecting off the copper-colored walls. A monk sat at his small writing table hunched close to the flame. A wooden bed with no mattress stood in a far corner, a dusty crucifix suspended over the headrest.

The monk dipped his quill in ink, crouched closer to the parchment and wrote the final sentences of his letter: “I am determined to drive them out. We must rid the land of their miasmic presence. There will be no sorcery here after I complete my studies.”

He signed the letter “Marin Mersenne,” folded it twice and slid it under his Bible. Then he crossed himself and took another sheet from the corner of his table and began: “Dear Fermat, in the past week I have been investigating multiperfect numbers. I recently made the discovery that...”

It would take Mersenne many hours to catch up on his correspondence. But after thirty minutes of writing he paused to light another candle, then tapped his quill against his chin. He tugged at the collar of his robe and bent to the parchment once again.

Another two hours passed and finally he placed the letter with the others. He blew out the candle, stood and went to his bed in the darkness. Kneeling, he folded his hands to pray, and his whispered words filled the dark cell.

* * *

“But we must do something about the sorcery that is spreading,” said Mersenne.

The Abbot paced behind his desk, hands clasped behind his back. Mersenne could see his knuckles turning white. “Are there really that many sorcerers to worry about, Marin?”

“Yes. And the worst thing is they look to various magicians documented in the scriptures for inspiration. They extrapolate upon whatever esoteric biblical accounts they can find and distort the facts beyond reason.”

The Abbot stopped pacing. He looked out his window to the fields behind the monastery. “Continue, Marin. Tell me more.”

“Well, the sorcerers study apocalyptic scriptures and attempt to work their magic in the most vile ways. They are beginning to exert an influence over the common people. We must do everything we can to wipe out their witchcraft as soon as possible.”

The Abbot turned to Mersenne, his brow furrowed: “But shouldn’t we focus on more immediate concerns? Feeding the poor. New methods of irrigation. Spreading the Word of God. Perhaps we shouldn’t focus so much on the negative.”

“Those things are very important, of course.” Mersenne cleared his throat. “But if we do not deal with the rampant Satanism spreading, there will only be dire consequences. The sorcerers are becoming too powerful, too plentiful. Lately I have spent much time studying various ways to invalidate their magic and to convince the common people that the sorcerer’s actions are the devil’s work.”

The Abbot sat down. He leaned forward and propped his elbows on his desk. “I want you to continue your scientific work, Marin. But I will no longer permit you to study ways to fight sorcery or witchcraft. You must quit this obsession with Satanism. It isn’t healthy.”

“But...”

“No. I will not provide any reasons for my decision, because I won’t consider any of your protests.”

Marin stared into the Abbot’s eyes. He looked into them for a long time. He did not understand the decision, but knew he had to obey. He stood and retied the black cord girding his robe, then looked at the Abbot again. He knew the decision was final, so he quickly turned and left.

* * *

Walking through the countryside, Mersenne stared at the hundreds of rabbits that lay slaughtered in the fields. “Evil,” he whispered, then lowered his head and tucked his bundle of letters closer to his side.

Some of the rabbits were still alive. They squealed and kicked up dust in the fields and Mersenne covered his ears and looked away. But then his eyes went back to the rabbits. Row after row of them. Mostly dead but a few still shaking and kicking.

He passed the fields and came to three small hills covered with tall grass. Large circles were burnt into the hillsides. Black rings with grey smoke rising from the centers. He crossed himself and recited, “The Lord is my shepherd; I shall not want. He maketh me to lie down in green pastures...” Then he quickened his step down the dirt road.

He came to six wooden crosses that he’d never noticed before. They came to his shoulders and were partially burnt. Drops of blood were dripping down the sides, bright red liquid spreading down the black, forming puddles on the ground.

“Where is this evil coming from?” Mersenne asked.

He shut his eyes tightly, squeezed his bundle closer and began to run.

* * *

Two pots of ink sat at the corner of his table. A pile of manuscripts and a stack of blank parchment at the other. The table teetered with thin strips of wood tucked under the legs. He was surprised it had stayed upright so many years. He looked at the pattern in the wood grain, thought for a moment, then glanced to the crucifix above his bed.

He smiled, bent forward and wrote, “Concerning numbers of the form N = 2p-1, p must be prime for N to be prime. This is easy to show with elementary algebra. But I will make this claim: For N to be prime, these values of p are necessary: 2, 3, 5, 7, 13, 17, 19, 31, 67, 127, 257, with no others less than 257.”

Mersenne was writing to Frenicle de Bessy on the material that would be in his next book. For many years Mersenne had searched for a formula that would produce every consecutive prime number, and now he felt he was on the verge of a breakthrough.

While working on the formula, he had arrived at a conjecture for the sequence of p values that made 2p-1 prime. He planned to include the material in the fourth chapter of his book.

Even though he could not test the values directly, he felt fairly confident the sequence was correct. He and Frenicle had discussed a primality testing method for several months and had developed a secret algorithm they had not revealed to their other correspondents. They both had doubts about the proof underlying the process, however; they suspected it wasn’t fully rigorous.

He wrote another paragraph, then finished with the line, “I hope one of us will soon find the missing step to prove the foundation of our algorithm. I think the formula for producing every consecutive prime is well within our grasp. But even if we do not locate the missing step, surely a formula that produces only primes (even if they are not consecutive) will soon be attainable.”

He signed the letter, folded it twice and placed it at a far corner. He rose from the table, went to his bed and lifted a Bible from his pillow, along with a copy of Arithmetic, by Diophantus, which lay beside it. Then he turned and shuffled out of his cell.

* * *

A crowd of monks were gathered at the large tree behind the monastery. Mersenne stood watching them from his window. A few were standing and crossing themselves while others bowed and glanced up into the branches of the tree. They were pointing at something. Mersenne walked through the monastery and went out to the group and looked up at the tree.

The Abbot was swaying there among the twisted branches. Suspended by a thick rope encircling his neck. Dead rabbits were hanging next to him, frayed twine around their midsections. The Abbot’s limbs were broken, bent backward against the joints unnaturally. Strings of meat were dangling from his throat. Mersenne counted six holes punctured in his lower abdomen, his intestines pulled out and hanging. The bloody cords swayed next to the dead rabbits.

A monk next to Mersenne began to weep while others pointed and talked in low voices. Marin looked at the Abbot again and noticed that his feet were missing. Hacked off at the ankles. He searched the ground but could not see them. He lowered his head and crossed himself, then slowly walked back to his cell.

Once in his cell, he got down on the floor and lay on his stomach. He began reciting Matthew 10:1 — “And when he had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease.”

He quoted other scriptures and mixed them with short prayers. He kept his eyes shut and pressed his palms against the cool floor. Then he felt a presence in the room.

A strong evil presence.

He opened his eyes and felt a force pulling his attention upward. He tried to resist. But the presence was too powerful. His head started to rise involuntarily and he strained to pull it down. But he was forced to yield to the presence. He pushed himself up, leaned back on his knees and blinked until his vision adjusted. He saw a small figure hovering in the air next to his crucifix.

A tiny man. Elvish, yet possessing evil facial features: yellow eyes, a long crooked nose. He floated and swayed in the air, dressed in a black robe with green designs. A silver necklace with symbols Mersenne had never seen before dangled from his neck. He was cradling something in his thin arms. Mersenne squinted, trying to see what it was.

A creature.

Definitely not human.

The small man held it with care as if it were his child. Mersenne got to his feet and stared into the elvish man’s face, then looked at the creature. It seemed to have too many limbs and no eyes. It squirmed and moved its mouth unnaturally without making a sound.

“Marin Mersenne,” said the hovering man.

He nodded.

“You are trying to rid the land of sorcery.”

“Yes, I am.” His voice cracked a little; he cleared his throat.

“You will fail.” The little man grinned and swayed. “Our sorcery is too powerful and has spread too far.”

Marin crossed himself and looked at the creature squirming in the man’s arms. He tried to think of a response. Sweat dripped down his back and seconds passed. Finally he was able to force away his fear: “No. God will help me stop your sorcery. My studies will soon be able to drive your kind from the Earth.”

The sorcerer hovered; his yellow eyes went to the crucifix on the wall. He opened his mouth to speak but Mersenne interrupted him: “Did you kill the Abbot?”

The man laughed, then changed subjects: “You think you’re a scientist, don’t you, Mersenne?”

Marin narrowed his eyes.

“Do you think you’re a scientist, or not? Answer me.”

“I am a monk.”

“But in your heart you desire to be a scientist.”

“You have no idea what is in my heart.”


Proceed to part 2...

Copyright © 2008 by Jason Earls

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