1-Butene polymer and molded product consisting of the polymer

1-butene based polymer satisfying the following (1′) to (4′);

• (1′) Crystalline resin having melting point (Tm), not observed or in the range of 0 to 100° C., wherein said melting point defined as the peak top of the maximum peak of the melting heat absorption curve obtained by heating a sample of said polymer at a rate of 10° C./minute using the Differential Scanning Calorimeter (DSC), after melting said sample in advance at 220° for 3 minutes under nitrogen atmosphere, followed by cooling it to −40° C. at a rate of 10° C./minute, and keeping it at −40° C. for 3 minutes.
• (2′) Stereoregularity index {(mmmm)/(mmrr+rmmr)}is at most 20.
• (3′) Molecular weight distribution (Mw/Mn) measured by Gel Permeation Chromatography (GPC) method is at most 4.0.
• (4′) Weight average molecular weight (Mw) measured by GPC method is in the range of 10,000 to 1,000,000.

1-butene based polymer satisfying the following (1″) to (4″);

• (1″) Crystalline resin having melting point (Tm−P), not observed or in the range of 0 to 100° C., wherein said melting point defined as the peak top of the peak observed in the highest temperature zone of the melting heat absorption curve obtained by heating a sample of said polymer at a rate of 10° C./minute using Differential Scanning Calorimeter (DSC), after melting said sample in advance at 190° for 5 minutes under nitrogen atmosphere, followed by cooling it to −10° C. at a rate of 5° C./minutes, and keeping it at −10° C. for 5 minutes.
• (2″) Stereoregularity index {(mmmm)/(mmrr+rmmr)} is at most 20.
• (3″) Molecular weight distribution (Mw/Mn) measured by Gel Permeation Chromatography (GPC) method is at most 4.0.
• (4″) Weight average molecular weight (Mw) measured by GPC method is in the range of 10,000 to 1,000,000.

Polyolefin based resin composition comprising 1 to 99 weight % of 1-butene based polymer [I] and 99 to 1 weight % of polyolefins [ II ], wherein said 1- butene based polymer [I] satisfies the following (1″) to (4″):

• (1″) Crystalline resin having melting point (Tm−P), not observed or in the range of 0 to 100° C., wherein said melting point defined as the peak top of the peak observed in the highest temperature zone of the melting heat absorption curve obtained by heating a sample of said polymer at a rate of 10° C./minute using Differential Scanning Calorimeter (DSC), after melting said sample in advance at 190° for 5 minutes under nitrogen atmosphere, followed by cooling it to −10° C. at a rate of 5° C./minutes, and keeping it at −10° C. for 5 minutes.
• (2″) Stereoregularity index {(mmmm)/(mmrr+rmmr)} is at most 20.
• (3″) Molecular weight distribution (Mw/Mn) measured by Gel Permeation Chromatography (GPC) method is at most 4.0.
• (4″) Weight average molecular weight (Mw) measured by GPC method is in the range of 10,000 to 1,000,000.

1-butene based resin composition comprising 1-butene based polymer satisfying (1″) to (4″) below, to which at least 10 ppm of nucleating agent is added.

• (1″) Crystalline resin having melting point (Tm−P), not observed or in the range of 0 to 100° C., wherein said melting point defined as the peak top of the peak observed in the highest temperature zone of the melting heat absorption curve obtained by heating a sample of said polymer at a rate of 10° C./minute using Differential Scanning Calorimeter (DSC), after melting said sample in advance at 190° for 5 minutes under nitrogen atmosphere, followed by cooling it to −10° C. at a rate of 5° C./minutes, and keeping it at −10° C. for 5 minutes.
• (2″) Stereoregularity index {(mmmm)/(mmrr+rmmr)} is at most 20.
• (3″) Molecular weight distribution (Mw/Mn) measured by Gel Permeation Chromatography (GPC) method is at most 4.0.
• (4″) Weight average molecular weight (Mw) measured by GPC method is in the range of 10,000 to 1,000,000.