13G Filing: James E. Flynn and Biocryst Pharmaceuticals Inc (BCRX)

SECURITIES
AND EXCHANGE COMMISSION

WASHINGTON,
DC 20549

SCHEDULE
13G

(Rule 13d-102)

INFORMATION TO BE INCLUDED IN STATEMENTS
FILED PURSUANT

TO RULES 13d-1(b)(c), AND (d) AND AMENDMENTS
THERETO FILED

PURSUANT TO RULE 13d-2(b)

(Amendment No.  ) *

BioCryst
Pharmaceuticals, Inc.

(Name of Issuer)

Common Stock

(Title of Class of Securities)

09058V103

(CUSIP Number)

May 25, 2017

(Date of Event Which Requires Filing of
this Statement)

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

☐  Rule 13d-1(b)

☒  Rule 13d-1(c)

☐  Rule 13d-1(d)

(Page 1 of 11 Pages)

———-

* The remainder of this cover page shall be filled out for a
reporting person’s initial filing on this form with respect to the subject class of securities, and for any subsequent amendment
containing information which would alter the disclosures provided in a prior cover page.

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 Securities Exchange Act of
1934 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).