Tupper's number

Tupper's number is the 544-digit number that makes Tupper's self-referential formula work - I call it "Tupper's number". Tupper's self-referential formula is a formula that, when graphed, can visually reproduce the formula itself - however upon further examination it's really more of a magic trick. Here's how it works:

Start with the formula:

1/2 < [mod([y/17]2-17[x]-mod([y],17),2)], where [ ] is the floor function (properly noted as [ ] with the tops removed) and mod(x,y) is the modulo function

Let N = the 544-digit number:

4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407 8569197543265718554420572104457358836818298237541396343382251994521916512843483329051311931999535024137587652392648746133949068701305622 9581321948111368533953556529085002387509285689269455597428154638651073004910672305893358605254409666435126534936364395712556569593681518 4334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300

When graphing the set of points (x,y) satisfying the inequality, in the area of the graph where 0<x<106 and N<y<N+17, the graph, when turned upside down, produces the formula:



This may seem amazing, but actually this formula is a lot more like the infinite monkey theorem (states that a monkey pressing random keys on a typewriter will eventually be produce any text) than a self-referential formula. The formula, as it turns out, can graph anything depending on what value of N you pick!

And also, think back to the instructions for the formula. In particular, take note that it requires making use of a specific 544-digit number, not just the formula itself! Because of this, the graph shown above of the formula is not so much in the formula as it is in the definition of the 544-digit number. This means that the formula isn't so much of a self-referential formula as it is a "magic trick" so to speak.

Written
4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024 9151191104116057391774078569197543265718554420572104457358836818298237541396343382251994521916512843483329051311 9319995350241375876523926487461339490687013056229581321948111368533953556529085002387509285689269455597428154638 6510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554 519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300