Propylene-based polymer

A propylene-based polymer comprising a propylene represented by the following characteristics (1) to (3):

• (1) the weight-average molecular weight Mw is from not smaller than 5,000 to less than 1,000,000 as measured by GPC;
• (2) 13C-NMR peaks derived from the carbon atom in a methyl group in a propylene unit chain formed by head-to-tail bond are observed and, wherein when the chemical shift of the top of a peak assigned to a pentad represented by mmmm is 21.8 ppm, the ratio of the area S5 of the peak having its top at 21.8 ppm to the total area S of peaks appearing within a range of from 19.8 ppm to 22.2 ppm is from not smaller than 10% to not greater than 60%, and, wherein when the area of a peak having its top at 21.5 to 21.6 ppm is S6, the relationship 4+2S5/S6>5 can be established;
• and
• (3) regio irregular units based on 2,1-inserted propylene monomer and/or 1,3-inserted propylene monomer are present in its main chain and the sum of the ratio of regio irregular units based on 2,1-insertion and 1,3-insertion to all propylene insertions is not smaller than 0.05%;
• wherein the propylene-based polymer has no melting point.