Source. Bajpai--Bennett--Chan, accepted author manuscript (June 26, 2023), pp. 3--4 and 14. This is the later manuscript example associated with $2P_1-6P_2+T_2$; arXiv v1 instead prints a larger example associated with $14P_1-8P_2+T_1$.

Statement. The accepted manuscript gives a four-term progression with initial term

1941933115377551077587122551830475057213069529860027159207864676
07518456158647255738252174690341489845812095405465699621251448104527
6691804469093296671884340486000359836438119479856969366457

and positive common difference

264015496910372571453683338480432534892486865509162672828630181
232132015211487807492449285089616569784339663505966152854290768706
31639734824690430160038942642966756875188627215486028565587784

The initial term has 190 digits and the common difference has 191 digits. The four terms have signature $[73,1,1,1]$: the first is $73^3$ times a square and the other three are squares. All six pairwise gcds are $1$.

Verification. Exact integer arithmetic in the verification script checks the three square roots, the square quotient by $73^3$, $\gcd(N,d)=1$, and every pairwise gcd. It also reproduces the finite congruence calculation underlying the infinite family. Independent reconstruction from the stated elliptic-curve point shows that the printed example arises after dividing a raw progression with common factor $4$ and reversing it. This explains why the $73^3$ term occurs first here although Proposition 5.2 writes it last; the transformation is not stated explicitly in the manuscript. From the repository root, uv run --no-sync python library/diophantine_problems/bajpai_2024_arithmetic_progressions_squarefull_numbers/evidence/verify_937_bajpai_examples.py runs every named obligation in well under one second and exits nonzero on any failed check, including under python -O.

Historical note. The manuscript calls this its smallest known example, not a proved minimum. Bennett--Walsh subsequently published a 111-digit record example.

Bears on. #937.