A vacuum pump , in particular a turbomolecular vacuum pump , comprising at least one Holweck pump stage having an inlet (E) and an outlet (A) in the pump direction downstream of the inlet (E), wherein the Holweck pump stage comprises a Holweck rotor having a rotor sleeve and a Holweck stator having a stator sleeve which is arranged coaxially to the Holweck rotor while forming a Holweck gap , wherein the stator sleeve has a Holweck thread having a plurality of thread grooves which are bounded by webs formed at the stator sleeve and by a groove base formed by the stator sleeve ; wherein the stator sleeve is formed in one piece and at least one thread parameter of the Holweck thread from the group of thread parameters, which consists of the number of webs , the thread pitch, the width of the thread grooves , the width of the webs and the height of the webs above the groove base , changes over the axial extent of the stator sleeve ; wherein the Holweck thread comprises a first threaded section (I) which extends in the axial direction over a first height dimension of the stator sleeve ; downstream of the first threaded section (I), a second threaded section (II) which extends in the axial direction over a second height dimension of the stator sleeve ; and, downstream of the second threaded section (III), at least a third threaded section (III) which extends in the axial direction over a third height dimension of the stator sleeve , wherein at least one threaded section of the three threaded sections (I, II, III) differs from another one of the three threaded sections (I, II, III) by at least one thread parameter from the group of thread parameters, characterized in that the number of webs in the first threaded section (I) is greater than in the second threaded section (II), with the number of webs in the first threaded section (I) being the same as the number of webs in the third threaded section (III). wherein the stator sleeve is formed in one piece and at least one thread parameter of the Holweck thread from the group of thread parameters, which consists of the number of webs , the thread pitch, the width of the thread grooves , the width of the webs and the height of the webs above the groove base , changes over the axial extent of the stator sleeve ; wherein the Holweck thread comprises a first threaded section (I) which extends in the axial direction over a first height dimension of the stator sleeve ; downstream of the first threaded section (I), a second threaded section (II) which extends in the axial direction over a second height dimension of the stator sleeve ; and, downstream of the second threaded section (III), at least a third threaded section (III) which extends in the axial direction over a third height dimension of the stator sleeve , wherein at least one threaded section of the three threaded sections (I, II, III) differs from another one of the three threaded sections (I, II, III) by at least one thread parameter from the group of thread parameters, characterized in that the number of webs in the first threaded section (I) is greater than in the second threaded section (II), with the number of webs in the first threaded section (I) being the same as the number of webs in the third threaded section (III). <EOS>