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Block #936,110

2CCLength 11β˜…β˜…β˜…β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 2/14/2015, 1:12:02 PM Β· Difficulty 10.9010 Β· 5,890,650 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
922afea2b9266a6403db6d83a207ba53aa928d6eaa56880890b41ed813cdfdc5
View on Chainz β†—

Height

#936,110

Difficulty

10.901043

Transactions

2

Size

432 B

Version

2

Bits

0ae6aac5

Nonce

75,460,194

Timestamp

2/14/2015, 1:12:02 PM

Confirmations

5,890,650

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a228bb26e5b222f1ea87e64d053f8264bff8158f306dded2b03635e1c04f7b53
Transactions (2)
Coinbase0ffe03bf460ac8…35545dffdb88ed
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
4394ca15305de9…3dfbb0bb31d69c
1 in β†’ 2 out3.9900 XPM226 B
AbWoBsCv…aWH9qWxwAGuc7HvN…FmAECz2x
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.865 Γ— 10⁹⁡(96-digit number)
28651788143081663434…13689476779272975441
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.865 Γ— 10⁹⁡(96-digit number)
28651788143081663434…13689476779272975441
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
5.730 Γ— 10⁹⁡(96-digit number)
57303576286163326869…27378953558545950881
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
1.146 Γ— 10⁹⁢(97-digit number)
11460715257232665373…54757907117091901761
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
2.292 Γ— 10⁹⁢(97-digit number)
22921430514465330747…09515814234183803521
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
4.584 Γ— 10⁹⁢(97-digit number)
45842861028930661495…19031628468367607041
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
9.168 Γ— 10⁹⁢(97-digit number)
91685722057861322991…38063256936735214081
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.833 Γ— 10⁹⁷(98-digit number)
18337144411572264598…76126513873470428161
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
3.667 Γ— 10⁹⁷(98-digit number)
36674288823144529196…52253027746940856321
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
7.334 Γ— 10⁹⁷(98-digit number)
73348577646289058393…04506055493881712641
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
1.466 Γ— 10⁹⁸(99-digit number)
14669715529257811678…09012110987763425281
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
11
2^10 Γ— origin + 1
2.933 Γ— 10⁹⁸(99-digit number)
29339431058515623357…18024221975526850561
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜†β˜†
Rarity
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,858,239 XPMΒ·at block #6,826,759 Β· updates every 60s
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