To provide propylene random copolymers capable of producing films excellent in low temperature heat-sealing properties, free of surface tackiness and excellent in antiblock properties, slip characteristics and rigidity as well or the like without adversely affecting the properties inherent in polypropylene films and compositions thereof.

In a copolymer of propylene and 1-butene, the copolymer is characterized in that the melting point [Tm(°C)] of the copolymer measured by a differential scanning calorimeter and the content [α(mol.%)] of the 1-butene units in the copolymer satisfy the formula: Tm≤160-3α and the crystallization temperature [Tc(°C)] of the copolymer measured by a differential scanning calorimeter and the melting point [Tm(°C)] satisfy the formula : Tc≥0.75Tm-10.