My grandmother[1] was a political prisoner and her favourite pastime while in prison was poetry. Since the inmates weren't allowed to have any possessions, not even a strip of paper, she composed poems in her head. She later published them in a poetry collection and I know people who memorized the entire collection. She herself had a phenomenal memory for poetry. Her friends would often call and ask for her to tell them the lyrics of old songs and poems, and even in her late 70s she never failed to answer their request without consulting her library. My mum once challenged her and asked her to recite the 50 minute-long Máj[2]. If she weren't interrupted after 10 minutes, she probably would have recited the entire thing. She was able to memorize a poem after hearing it just once and it seemed that she retained poems indefinitely. I don't know whether this talent was the result of 6 years in an environment where memory is the only means to persist information, but it seems likely that it played a role.
Another less impressive anecdatum is my own experience of about a year with a phone that couldn't remember phone numbers. In the beginning I memorized numbers out of necessity. By the end of the year I had a mental address book of about 30 numbers and new numbers could be added effortlessly. The bewildered looks of people giving me their number without me pulling out a phone to write it down were priceless.
In ancient Indian mathematics, people would compose poetry based on tables of numbers, so that things such as sine tables, and the value of pi up to certain number of decimal places, were easier to remember [1]. A delightful example given in the site is "Milk is best for breakfast, when it is morning, it should be stirred. But Gopālan says there is no milk - the number of days of English months in order.", which in the appropriate alphabet, represents the number of days in the months of the Gregorian calendar.
There’s a literary organization/movement called Oulipo[1] that similarly works with patterns and algorithms to creatively restrict or generate writing.
"How I need a drink, alcoholic of course, after the heavy lectures involving quantum mechanics" gets you a few digits further (but of course yours is plenty accurate for calculating)
When you memorized numbers that way, did you "see" the numbers in your mind's eye? And when you went to recall it, did you basically read it from that impression? I sometimes memorize numbers and other strings that way.
It feels as though I simultaneously remember and recall an image of the number as well as its numeric value. What helps me remember the numeric value is identifying its interesting properties and patterns.
This mental phone book improved my ability to memorize other types of random strings. On one occasion I memorized a 20-digit hexadecimal license key, though I had to read it about three times. The client who watched as I keyed it in was very impressed. On a second thought it isn't that impressive given it's 12 digits short of a UUID.
Not the GP, but for me, in the context of numbers that I use on a keypad (or, ahem, in the context of a rotary dial), the physical actions are linked into the memorization, along with some combination of aural and visual memory.
Another less impressive anecdatum is my own experience of about a year with a phone that couldn't remember phone numbers. In the beginning I memorized numbers out of necessity. By the end of the year I had a mental address book of about 30 numbers and new numbers could be added effortlessly. The bewildered looks of people giving me their number without me pulling out a phone to write it down were priceless.
[1]: https://cs.wikipedia.org/wiki/Bo%C5%BEena_Kuklov%C3%A1-J%C3%...
[2]: https://www.youtube.com/watch?v=jjoX5y_JZ40