\$ 110728750366081 = 37 \times 41 \times 71 \times 661 \times 673 \times 2311 \$ is wrongly recognized as a prime.
Try it online!
Sisyphus implemented the Solovay-Strassen primality test, which is based on a theorem by Euler which states for any prime number \$p\$ and any integer \$a\$:
$$
a^{p-1\over2} \equiv \left({a \over p}\right) \mod p,
$$
where \$\left({a \over p}\right)\$ is the Jacobi symbol. The primality test usually draws a few random numbers for \$a\$ and assumes \$p\$ is a prime if the equality was satisfied for all \$a\$.
Because randomness doesn't work very well with cops-and-robbers, the long constant hardcodes a fixed set of values for \$a\$:
2, 3, 5, 7, 11, 13, 17, 19, 11617, 15493, 16433, 25919, 31091, 31469, 49307, 55001, 55399, 65071
For a given \$a\$ there exist composite numbers that satisfy the equivalence, these are called Euler-Jacobi Pseudoprime to base \$a\$.
To solve the challenge, one needs to a find a single positive integer that is a Euler-Jacobi Pseudoprime to all the bases. Bruteforcing this turned out to be infeasible, but this article mentions that some Carmichael numbers are Euler-Jacobi Pseudoprime to some base. By filtering a list of Carmichael numbers from this site¹, I was able to find a few solutions:
110728750366081 37*41*71*661*673*2311
237382308072001 29*101*127*337*631*3001
549022047900481 29*31*199*857*1381*2593
815369599393441 179*5741*6673*118903
1777021736490001 71*79*199*461*3453451
2409992788323121 29*67*499*20693*120121
5514474572006401 1051*2521*11551*180181
6036890513068801 43*71*101*40129*487873
9704292238761121 79*113*521*631*937*3529
14988701359951201 191*241*271*401*1051*2851
23456937465858961 37*43*71*103*181*821*13567
23880657211210801 23*61*109*157*271*937*3917
26055899070788161 31*173*433*1777*2437*2591
28365866503643761 43*53*137*281*443*457*1597
30908877197436001 421*601*1429*1709*50021
33834184755920641 29*37*71*73*97*547*114661
45561504118095001 211*421*751*3571*191251
51176905599093121 29*31*43*67*137*6427*22441
64612622789870401 97*181*277*647*691*29717
83629862695874881 181*881*953*4789*114913
132132263067090001 41*131*647*47501*800473
162098861806081201 71*421*2393*11047*205141
219842309289002401 23*29*71*151*337*3851*23689
283029750046243201 47*101*113*691*21841*34961
308601054690500881 29*37*41*331*691*4621*6637
314618527970346601 991*1093*3511*3571*23167
317711413912838401 43*53*73*79*113*3361*63649
397597753071953281 73*211*241*271*8317*47521
406954063186624801 29*37*41*191*3037*3221*4951
507180584040530401 89*163*281*397*463*743*911
511311312146194561 37*79*131*353*577*1361*4817
594232587298120681 29*71*127*1163*1171*1668629
650151107946325441 547*6553*35491*5110561
682696543350931201 315011*882029*2457079
685726732138361761 67*331*397*487*1567*102061
738294418360350721 89*353*5897*14081*283009
794134562259598561 23*79*89*157*241*2341*55441
806936176399473121 53*137*157*2731*4409*58787
830121613337016001 73*109*34651*53353*56431
963141865421809921 23*43*61*113*193*353*617*3361
¹The files are not actually gzipped, they are just plain text files