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Block #324,758

2CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 12/22/2013, 1:36:35 PM Β· Difficulty 10.2069 Β· 6,500,192 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7f9ae2986b8fcb99de4e750f687ce51905434a51e2de9518899ee39673c19dc
View on Chainz β†—

Height

#324,758

Difficulty

10.206942

Transactions

2

Size

426 B

Version

2

Bits

0a34fa2a

Nonce

342,059

Timestamp

12/22/2013, 1:36:35 PM

Confirmations

6,500,192

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

e0c9d20fd7a39bb059e3623e4ee5bf3e9444360a56489077d621673069f12f7c
Transactions (2)
Coinbase5ec11a29920937…620b02e5bcae13
1 in β†’ 1 out9.5900 XPM110 B
AeKNrjNj…1NEq95Ta
77dff8d999df31…28d0a7352cbde8
1 in β†’ 2 out34.6601 XPM225 B
AKn34GE2…5TdATz9uASPsJqmz…6icdPJPa
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.

8.471 Γ— 10⁹⁢(97-digit number)
84711583238274575790…22588031821049591201
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
8.471 Γ— 10⁹⁢(97-digit number)
84711583238274575790…22588031821049591201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
1.694 Γ— 10⁹⁷(98-digit number)
16942316647654915158…45176063642099182401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
3.388 Γ— 10⁹⁷(98-digit number)
33884633295309830316…90352127284198364801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
6.776 Γ— 10⁹⁷(98-digit number)
67769266590619660632…80704254568396729601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
1.355 Γ— 10⁹⁸(99-digit number)
13553853318123932126…61408509136793459201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
2.710 Γ— 10⁹⁸(99-digit number)
27107706636247864253…22817018273586918401
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
5.421 Γ— 10⁹⁸(99-digit number)
54215413272495728506…45634036547173836801
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
1.084 Γ— 10⁹⁹(100-digit number)
10843082654499145701…91268073094347673601
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
2.168 Γ— 10⁹⁹(100-digit number)
21686165308998291402…82536146188695347201
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
10
2^9 Γ— origin + 1
4.337 Γ— 10⁹⁹(100-digit number)
43372330617996582804…65072292377390694401
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:57,843,678 XPMΒ·at block #6,824,949 Β· updates every 60s
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