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Block #1,374,372

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/18/2015, 2:05:20 PM Β· Difficulty 10.8083 Β· 5,452,387 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0540ae28b3f4bfc10b9899431b3649301dac225c87fe764a4d2de5ef4e8ad615
View on Chainz β†—

Height

#1,374,372

Difficulty

10.808328

Transactions

2

Size

574 B

Version

2

Bits

0aceee91

Nonce

282,775,819

Timestamp

12/18/2015, 2:05:20 PM

Confirmations

5,452,387

Mined by

⛏️ P2SHALeop52tgjTNFGomkdMvoRMJTg9oDdCxvh

Merkle Root

c7238956eb9695243bb5ffc19b2ee3656fa5c3f77758a59e45f5cf61b8bdedf8
Transactions (2)
Coinbase85e5c43fc8133d…b5eab3eee6a60d
1 in β†’ 1 out8.5600 XPM109 B
ALeop52t…9oDdCxvh
a8d950dea3a54a…bdb8a7eaa6c8b8
2 in β†’ 2 out23.9900 XPM375 B
AQCBKY8Q…22Z934WMAQ6ABXxb…MUBBdSA9
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.

1.447 Γ— 10⁹⁴(95-digit number)
14471800883343218572…45832908644883816001
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
1.447 Γ— 10⁹⁴(95-digit number)
14471800883343218572…45832908644883816001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
2.894 Γ— 10⁹⁴(95-digit number)
28943601766686437145…91665817289767632001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
5.788 Γ— 10⁹⁴(95-digit number)
57887203533372874291…83331634579535264001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.157 Γ— 10⁹⁡(96-digit number)
11577440706674574858…66663269159070528001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
2.315 Γ— 10⁹⁡(96-digit number)
23154881413349149716…33326538318141056001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
4.630 Γ— 10⁹⁡(96-digit number)
46309762826698299432…66653076636282112001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
9.261 Γ— 10⁹⁡(96-digit number)
92619525653396598865…33306153272564224001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.852 Γ— 10⁹⁢(97-digit number)
18523905130679319773…66612306545128448001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
3.704 Γ— 10⁹⁢(97-digit number)
37047810261358639546…33224613090256896001
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
7.409 Γ— 10⁹⁢(97-digit number)
74095620522717279092…66449226180513792001
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,858,231 XPMΒ·at block #6,826,758 Β· updates every 60s
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