Linnik's constant

Upper bound, last-listed row

| $5$ | [[XylDiss2011](#XylDiss2011)] | Attributed in modern literature to Xylouris's 2011 dissertation. [MMT2024-ub-5] |

exact pinned row

| $5$ | [[XylDiss2011](#XylDiss2011)] | Attributed in modern literature to Xylouris's 2011 dissertation. <a href="#MMT2024-ub-5">[MMT2024-ub-5]</a> |

tracked since 2026-07-24 — no movement seen yet

Lower bound, last-listed row

| $1$ | | Trivial: $P(1,q)\ge q+1$. |tracked since 2026-07-24 — no movement seen yet

Checked against material for its cited source

• Another row, not one shown above: bound row $20$ line 51 citing [Xyl2011] — the claim we checked: that Table 1 of the published paper (p. 65) lists 20 as Graham's 1981 value, which is all this row credits to Xyl2011. What we read supports it. This verdict does not cover whether Graham's 1981 work itself proves L ≤ 20. source link (read in the body of the published Acta Arithmetica paper, the publisher's own typeset PDF (IMPAN, free under CC-BY), printed p. 65, read from the page image). Selected: drawn by its position in the list of cited rows, not because it looked wrong.
• Another row, not one shown above: bound row $630$ line 45 citing [Xyl2011] — the claim we checked: that the cited 2011 paper lists the upper bound 630 in its historical table, credited to Jutila (1971), as the row's comment says. The row's second link, [Xyl2011-historical-table], is checked only for whether it points at that table. What we read supports it: Table 1 on p. 65, "Admissible values for L", lists 630 with the year 1971 and the author Jutila, and the row's second link points at that table. source link (read in the published edition, Acta Arithmetica 150, no. 1 (2011), the publisher's PDF, printed pp. 65, 66, 90 and 91, as page images). Selected: drawn by its position in the list of cited rows, not because it looked wrong.

2 bound row(s) here have been checked against material for their cited source (2 drawn by position, 0 chosen because something already looked wrong). Across this whole ledger 70 row(s) have been drawn by position, against 691 rows that name a source, counted on 2026-09-27: 64 were checked against material for their cited sources and for 6 the cited source could not be read at all. 5 more were chosen for suspicion and checked; they are counted apart, because a set selected for suspicion carries no rate. A row not listed here has NOT been checked.