Prime of Life

Admonition

“Primrose! Just what do you think you are doing, young lady?” Great Aunt Jane’s stentorian voice blared along the landing.

Primi’s hand fell limp from the doorknob.

“I’m… sorry, Aunt Jane. I just wanted to…”

“You know perfectly well you are forbidden to enter Great Uncle John’s office. It is off limits. You are seven years old and you know my rules. Now go to your room. I do not expect to see you until suppertime.”

Hot tears welling, Primi ran down the landing to her own room, slammed the door and threw herself face down on her bed, sobs racking her lean frame as the late afternoon sun streamed in through the south-facing window. 

Primrose Lovelace Byrne, Primi to her school friends and family, had lived with her Great Aunt Jane for as long as she could remember. Blonde, pretty and tall for her age, she had no parents, and only vague recollections. Aunt Jane had explained that Primi’s parents had died, when she was three years old, in a road accident in a place called Monaco, on one of their filming trips. Primi’s father had been an actor; her mother a movie director. They had never been short of work and Primi enjoyed watching their films online, far more than Great Aunt Jane did.

Blinking away tears of frustration, Primi reached for her iPad and resumed the movie she’d been watching, The Haunting by the Lake. The man she knew to have been her father stood before her on the screen, his loose cotton shirt open almost to his waist, exposing his six-pack and chest hair. The camera panned out to reveal the ghost, a rather poorly made-up fellow with black around his CGI-reddened eyes, the lights throwing his face into long shadows. Primi switched it off again, tossing the iPad onto the eiderdown.

The movie could wait. What Primi really wanted to know was, what was in Great Uncle John’s office, that Great Aunt Jane so badly wanted her never to see?

The house was enormous, with three storeys and a couple of acres of land. Great Aunt Jane spent a lot of time outdoors tending her beloved gardens. Primi preferred indoors, wandering the hallways and landings, getting to know housekeeper Mrs Holliday’s routines so she could avoid her. Primi knew her way around now. She loved the four staircases - the grand one from the main hall, the discreet carpeted stairway near the guest bedrooms, and the two stone stepped service stairwells at the rear corners of the edifice. Following her learned mental map, she could pop up anywhere, anytime, secure in her unpredictability.

Great Uncle John had been an antique dealer, Aunt Jane had told her. He bought and collected old things; objects that came with a story. There had been no internet at that time, so he’d done something called auction by mail. He’d put advertisements in newspapers, showing what he had to sell, and invited buyers to bid what they were prepared to pay, by a cutoff date which the bidder’s letter postmark had to be before. Then he would write to the highest bidder and accept their offer, if it was above the lowest price he could accept, after which he would mail them their purchase by parcel post.

Great Uncle John had died on the day Primi was born. Aunt Jane had never said much about his death, just that she missed him very much and they had been very happy together. “He got sick and passed away,” was as much as Primi could get from her great aunt. 

Primi was a bright child. Not just in the sense that every parent and guardian considers their child or ward to be a cut above average. Primi excelled in mathematics, routinely finishing her assignments with half the lesson left and all her answers correct. Her teachers had grown used to preparing extra challenges for her. Before long, she was setting her own challenges and vying with others to match her.

Opportunity

Now a confident, poised eleven-year-old, Primrose continued to enjoy the freedom of Aunt Jane’s house, having explored every corner of every floor to the satisfaction of her youthful curiosity. The attic rooms with their cobwebbed windows, stacks of junk and creaky floorboards fascinated her for a while but, eventually and inevitably, their appeal waned. Great Uncle John’s secret, undiscovered office ate at Primi day and night. She just had to know what was behind that door.

Aunt Jane spent longer and longer tending her herbs and plants, waking as dawn broke, returning to the house only to eat and, at weekends, to check via Mrs Holliday that Primi was safe, fed and gainfully occupied. From Primi’s school reports, Aunt Jane had ascertained that she continued to lead her peers in mathematics, to the extent that she was ready for challenges a year or more ahead of her grade level. The child had matured beyond recognition, Aunt Jane thought, since coming to live with her.

Primi did not fail to notice her great aunt’s gradual relaxation of the surveillance that had stifled her so, through her early formative years. If only adults understood the stifling, suffocating effect upon children of bedtimes, curfews and stupid household rules. Why was it so hard for adults to comprehend that children were the future of the world - that the young would be calling the tunes, after the old had faded away? However were Primi and her peers going to learn to run the show, if grown-ups kept stopping them doing everything, at every hand’s turn?

Primi knew where Aunt Jane kept the key to Uncle John’s office. The key rack, with labelled keys on hooks, was fixed to the wall behind Aunt Jane’s desk, in her housekeeping room behind the kitchen. A quick glance through the window, to confirm Aunt Jane’s presence in the southern herb garden, and she was away, light and lithe of step, pattering across the stone flags, through the heavy wooden door, into the centre of Aunt Jane’s controlled universe. Primi knew she should not be in here. She had better hurry, before Aunt Jane caught her.

Feeling incredibly naughty, Primi reached for the key labelled ‘John’s office’. A rather ordinary, grey, metal key, with a green plastic tab, she eagerly gripped its wicked heaviness as she hastened toward the forbidden room.

The key turned easily, as if the lock had just been oiled. Primi hesitated, turning guiltily behind her, in case Mrs Holliday or Great Aunt Jane might suddenly have appeared on the landing behind her. She saw only the dark, polished balustrade, the drugget carpet with its varnished oak borders and the wood panelled wall with its recessed doorways.

Primi swallowed and twisted the doorknob. With no resistance that she could detect, the door swung smoothly open. Inevitability propelled her forward and she was standing in Great Uncle John’s private office. 

Her first impression was that it didn’t look as though no-one used it any more. In the centre of the room was an oak desk, tall and imposing, with a brass-cornered blotter and a heavy, leather-bound volume upon it. A heavy, wooden swivel chair sat importantly behind the desk, with a lumbar cushion, compressed and indented from everyday use. It was as though Great Uncle John had just left, and may return at any moment.

The next thing Primi noticed was the safe, standing in the corner, between the diamond leaded window and the oak panelled wall. It was enormous. She knew it was a safe because it had a large combination lock wheel on its dark green metal door. She had seen combination safes before, so she knew this one was unusual. Normally the numbers went up to one hundred. This one had smaller divisions around its edge, counting all the way to two hundred. The knurled wheel was cold to her touch. Gingerly, she moved it clockwise. It felt oily and heavy, with a light clicking behind as it turned. What was the combination, she wondered. What was inside?

Her attention shifted to the desk, dominating the office. The blue leather-bound book sat square on the blotter. Primi tiptoed around to the chair side of the desk but she did not sit down. That would not be right. The chair, she was sure, would still be warm from the presence of Great Uncle John. She could see his indent in the cushions. It was his chair, not hers.

The cover of the book was heavy. As soon as she tipped it over, Primi could see it was a diary, of the journal (rather than engagements) type. She leafed through the pages, her interest piqued. Uncle John had evidently been interested in mathematics. There were entries about prime numbers - she’d learned about those at school, how they were like DNA fingerprints that showed familial relations between numbers. Skimming through her great uncle’s entries, Primi detected an interest in length of life, a topic he had returned to, again and again. Uncle John had mused upon his own inevitable death. “Pray tell me, dear old Father Time, shall I attain my twentieth prime?”

Primi had learned the first twenty prime numbers. She’d become fascinated with primes. In an earlier class, she’d been duped by a bored teacher into thinking the only notable fact about primes was they could not be divided by anything except one and themselves. How wrong she had been, she now saw. Prime numbers are the very building blocks of mathematics and of logic. All modern cryptography is based upon prime numbers. Without them, we can forget secure online banking and encrypted text messages. Primi knew that the twentieth prime number is 71.

 Great Uncle John had not attained his tentieth prime. He had died in his fifties - she must ask Aunt Jane exactly how old he had been.

Almost ready to leave, Primi flicked forward through the desk diary. Reaching the last page, she held her breath. There was a sort of poem.

In youthful bloom of primeth prime,

The num’rals whirl, ‘tis come the time.

The key shall count thy summers gone,

And those of she foreprimely born.

Complete the key as goes this rhyme,

With next the common primeth prime.

Take heed - ‘twill yield a single time,

Till primeth prime again align.

Primi read it twice. It didn’t make sense. She flipped the heavy cover closed and crossed back to the tall, imposing safe. Again, she spun the combination dial. It was the same heavy, oiled clicking, spinning slowly to a stop.

“Primrose!”

Oh, no. Caught in the act. Great Aunt Jane was there, in the doorway, arms folded.

“Explain yourself, this instant. What are you doing in your Great Uncle’s office, and what gives you the right to be in here?”

Coming of Age

Primrose was seventeen.

She’d never been into Uncle John’s office again, after the last time. Aunt Jane had grounded her in her room for a whole week, only out for meals and a fifteen-minute daily walk around the garden, with Aunt Jane holding her hand, as though she was five.

The intervening six years had passed cordially enough. Having punished Primi, Aunt Jane had not referred to the office incident again. Primi felt comfortable in her great aunt’s company. The old lady knew her stuff. Primi was studying Further Maths and she was surprised by how much Aunt Jane knew about the subject. Primi had felt inspired to research prime numbers for the elective part of her course. She had learned about Bell numbers, Leyland primes, illegal primes and - by far, the most intriguing - Primeth primes. The title of the last list chimed in her memory, from her great uncle’s rhyme, on the very last page of his diary.

Primi had won Great Aunt Jane over, although she had been sceptical at first. “Aunt Jane, if we could just look at Uncle John’s diary again, I’m sure I could make sense of the last page. Don’t you want to understand your husband’s last written thoughts?” At that, Aunt Jane had shot Primi a glance as vitriolic as it was brief. Then she had mellowed.

“All right. Let’s take a look.”

Combination

“Look, Aunt Jane. It says, ‘The key shall count thy summers gone.’ I’m seventeen, so the first number in the combination must be 17. Then, it says ‘those’ - that’s the summers gone, or the age - of ‘she fore primely born’. That’s you, Aunt Jane, because the gap between our ages is exactly fifty years, which make you sixty-seven, a prime number. And that’s not all - Uncle John’s rhyme talks about primeth primes. The prime numbers start with 2, then 3, 5, 7, 11, 13, 17, 19 and onward. So, 2 is the first prime. The primeth primes are prime numbers whose place in the sequence is itself a prime number. So, the first primeth prime is 3, because it’s at position 2 in the list, and 2 is a prime number.”

Great Aunt Jane nodded. “OK, I get you. You are 17, which is the seventh prime. A primeth prime. I am 67 which, if I am not mistaken, is the nineteenth prime - another primeth prime. Are you saying that makes our age difference special?”

Primi smiled. “It’s Uncle John saying that, not me. You should know him better than I do. Now, the combination fo the safe. We’ve got 17 and 67. Uncle John’s rhyme mentions the next common primeth prime. I think he meant common in the sense that it applies to us both. So, when will be the next time both our ages are primeth primes? I’ve checked; the next two primeth primes with a fifty-year gap are 59 and 109. That gives us the last two combination numbers.”

Again, Aunt Jane nodded, more slowly this time. “Well, I hope I’m still around at 109. Now, you have to spin a combination lock four times clockwise and stop at the first number, then three times the other way and stop at the second, and so on. I guess it makes sense that it goes up to 200, because the usual 100 wouldn’t be enough -“

Aunt Jane stopped and caught her breath.

Primi egged her on. “Don’t be scared, Aunt Jane. It’s what Uncle John wants us to do. I mean, wanted us to do.”

Both women snapped around to the leather chair, conscious of an almost imperceptible movement in the shadows. If interrogated at that moment, both Primi and her great aunt would have sworn they glimpsed, in their peripheral vision, a wiry man in a blue-grey suit, sitting back in the leather chair, regarding them with interest. There was nothing, of course - the chair was empty - although Aunt Jane was privately sure the man had been her late husband, and Primi was equally sure the cushions had been moved since she’d last seen them.

Primi reached out and turned the safe’s dial, the familiar oily click beneath her hand. Four times clockwise to 17, then three times back to 67, twice round clockwise to 59, then once back to 109.

The dial locked. The two women glanced toward each other before Primi reached out and pressed the heavy brass handle. The safe door swung open.

At first, both were sure the safe was empty. Then, Primi noticed the small, brown envelope. Impatiently she tore it open and read the note on the card inside.

Dear Primrose, your great Aunt is safe until the next time.

Twelve years later

Primrose was twenty-nine. Her great aunt was seventy-nine.

Soon after they had found the note in the safe, Aunt Jane had explained that her husband, Primi’s great uncle, had chosen her name. When the doctor confirmed they were expecting a little girl, Primi’s parents had asked the family for name ideas and had settled on Uncle John’s Primrose.

Neither woman had been able to fathom what Uncle John had meant by his handwritten note in the envelope.

At twenty-nine, having completed a Ph.D in mathematics and secured a lectureship at Cambridge, Primi felt she should be looking after her great aunt. However, the old lady didn’t seem to have aged a day since they’d opened Uncle John’s safe, whereas Primi herself was feeling decidedly dilapidated. Her shoulders ached when she got up in the morning and her knees cracked from time to time. She’d noticed one or two grey hairs. For all the world, she felt more like someone over forty than under thirty.

When next the primeth primes align

When Great Aunt Jane turned one hundred, she still looked and felt exactly as she had done at age sixty-seven. Primrose, aged fifty, boasted thinning white hair, bony hands, drooping, wrinkled jowls and a bent back. She felt more like a woman in her eighties than one of fifty.

Both women had concluded what was going on and had discussed it many times. All that mattered to them was that Primi should make it to 101 - she was obviously ageing at twice the normal rate, while Aunt Jane stayed fixed in her late sixties. Uncle John’s note made perfect sense now. 

What was special about 101? Well, as Primi had worked out, and Aunt Jane had agreed, Primi was ageing at two years for every one. The next time their ages would both be primeth primes would be fifty-nine (101 in apparent terms) for Primi and one hundred and nine for Aunt Jane. The elder woman made it her business to look after the younger, in her dotage.

The funeral over, Primi walked from Aunt Jane’s grave with sorrowful recollection. The safe had opened the second time, 42 years after the first, to the same combination. Instantly, the years had fallen from Primi, and in the same moment, Aunt Jane had breathed a relieved sigh, a seraphic smile on her lips, and passed on.