<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0206</schemaVersion>

    <documentType>3</documentType>

    <periodOfReport>2017-06-01</periodOfReport>

    <noSecuritiesOwned>0</noSecuritiesOwned>

    <issuer>
        <issuerCik>0001474432</issuerCik>
        <issuerName>Pure Storage, Inc.</issuerName>
        <issuerTradingSymbol>PSTG</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001331846</rptOwnerCik>
            <rptOwnerName>Sutter Hill Associates, LLC</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>755 PAGE MILL ROAD, SUITE A-200</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>PALO ALTO</rptOwnerCity>
            <rptOwnerState>CA</rptOwnerState>
            <rptOwnerZipCode>94304-1005</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 10% Owner Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeHolding>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <footnoteId id="F1"/>
            </conversionOrExercisePrice>
            <exerciseDate>
                <footnoteId id="F1"/>
            </exerciseDate>
            <expirationDate>
                <footnoteId id="F1"/>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Class A Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>1024538</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeHolding>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">Each share of Class B Common Stock is convertible at any time at the option of the reporting person into one share of Class A Common Stock and has no expiration date.  The Class B Common Stock will convert automatically into Class A Common Stock on the same basis upon the earlier of: (1) any transfer, whether or not for value, except for certain &quot;Permitted Transfers&quot; as defined in the Issuer's restated certificate of incorporation in effect as of the date hereof, (ii) the affirmative vote of the holders of Class B Common Stock representing not less than a majority of the outstanding shares of Class B Common Stock, or (iii) October 6, 2025.</footnote>
    </footnotes>

    <remarks>The reporting person acquired the shares reported herein in connection with the liquidation, on May 31, 2017, by a limited partner (the &quot;Limited Partner&quot;) of Sutter Hill Ventures, a California Limited Partnership (&quot;SHV&quot;) in return for its ratable share of the holdings of SHV (the &quot;Liquidation&quot;) including the shares of Class B Common Stock reported herein.  In connection with the Liquidation, on June 1, 2017, the reporting person and SHV collectively repurchased all of the shares of Class B Common Stock distributed to the Limited Partner.
The reporting person and SHV may be deemed to be members of a 10% stockholder group.</remarks>

    <ownerSignature>
        <signatureName>/s/ Robert Yin, Attorney-in-fact</signatureName>
        <signatureDate>2017-06-01</signatureDate>
    </ownerSignature>
</ownershipDocument>
