UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

WASHINGTON, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

(Amendment No.  )*

RhythmPharmaceuticals, Inc.

(Name of Issuer)

Common Stock, $0.001 par value per share

(Title of Class of Securities)

76243J105

(CUSIP Number)

February 1, 2024

(Date of Event Which Requires Filing of this Statement)

Check the appropriate box todesignate the rule pursuant to which this Schedule is filed:

☐ Rule 13d-1(b)

☒ Rule 13d-1(c)

☐Rule 13d-1(d)

The information required in the remainder of this cover page shall not be deemed to be “filed” for the purpose of Section 18 of the SecuritiesExchange Act of 1934 (“Act”) or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Rhythm Pharmaceuticals, Inc. (the “Issuer”)

222 Berkely Street, 12^th Floor

Boston, MA 02116

The names of the persons filing this report (collectively, the “Reporting Persons”) are:

Perceptive Advisors LLC (“Perceptive Advisors”)

Joseph Edelman (“Mr. Edelman”)

Perceptive Life Sciences Master Fund, Ltd. (the “Master Fund”)

The address of the principal business office of each of the Reporting Persons is:

51 Astor Place, 10th Floor

NewYork, NY 10003

Perceptive Advisors is a Delaware limited liability company

Mr. Edelman is a United States citizen

The Master Fund is a Cayman Islands corporation

Common stock, $0.001 par value per share (“Common Stock”)

76243J105

Not applicable.

The information required by this item with respect to each Reporting Person is set forth in Rows 5 through 9 and 11 of the cover page to thisSchedule 13G. The ownership percentages reported are based on an aggregate of 59,096,454 shares of Common Stock outstanding as of November 1, 2023, as reported by the Issuer in the Issuer’s Quarterly Report on Form 10-Q filed with the Securities and Exchange Commission on November 8, 2023.

The Master Fund directly holds 3,260,013 shares of Common Stock. Perceptive Advisors servesas the investment manager to the Master Fund and may be deemed to beneficially own shares held by the Master Fund. Mr. Edelman is the managing member of Perceptive Advisors and may be deemed to beneficially own the shares held by the MasterFund.

If this statement is being filed to report the fact that as of the date hereof the Reporting Persons have ceased to be the beneficial owner ofmore than five percent of the class of securities, check the following ☐.

Not applicable.

Not applicable.

Not applicable.

Not applicable.

By signing below I certify that, to the best of my knowledge and belief, the securities referred to above were not acquired and are not heldfor the purpose of or with the effect of changing or influencing the control of the issuer of the securities and were not acquired and are not held in connection with or as a participant in any transaction having that purpose or effect, other thanactivities solely in connection with a nomination under § 240.14a-11.

SIGNATURE

After reasonable inquiry and to the best of its knowledge and belief, each of the undersigned certifies that the information set forth in thisstatement is true, complete and correct.