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Block #334,520

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/29/2013, 1:48:33 PM Β· Difficulty 10.1562 Β· 6,469,411 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3c0834110464510ffeae2aba02c635e5e6b9e9f5662533b6c955e4b33db30aa1
View on Chainz β†—

Height

#334,520

Difficulty

10.156156

Transactions

2

Size

723 B

Version

2

Bits

0a27f9d9

Nonce

248,902

Timestamp

12/29/2013, 1:48:33 PM

Confirmations

6,469,411

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c5e78b3ff9f5652a7e039e891d3a3898700026952dce59f83a2fbe92944bcb4e
Transactions (2)
Coinbased66c6ae8c0d35c…91dcbb9c346765
1 in β†’ 1 out9.6900 XPM110 B
AeKNrjNj…1NEq95Ta
513dfdad049184…4b9f18ffe903a1
3 in β†’ 2 out25.3877 XPM522 B
AbJ2ok3V…ph5xRxkjALTyjC6q…UZt4ET2B
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.

1.095 Γ— 10⁹⁸(99-digit number)
10952678287287139134…70189915503199998079
Discovered Prime Numbers
p_k = 2^k Γ— origin βˆ’ 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 βˆ’ 1
1.095 Γ— 10⁹⁸(99-digit number)
10952678287287139134…70189915503199998079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.190 Γ— 10⁹⁸(99-digit number)
21905356574574278269…40379831006399996159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
4.381 Γ— 10⁹⁸(99-digit number)
43810713149148556538…80759662012799992319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
8.762 Γ— 10⁹⁸(99-digit number)
87621426298297113076…61519324025599984639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
1.752 Γ— 10⁹⁹(100-digit number)
17524285259659422615…23038648051199969279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
3.504 Γ— 10⁹⁹(100-digit number)
35048570519318845230…46077296102399938559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
7.009 Γ— 10⁹⁹(100-digit number)
70097141038637690461…92154592204799877119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.401 Γ— 10¹⁰⁰(101-digit number)
14019428207727538092…84309184409599754239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
2.803 Γ— 10¹⁰⁰(101-digit number)
28038856415455076184…68618368819199508479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
5.607 Γ— 10¹⁰⁰(101-digit number)
56077712830910152369…37236737638399016959
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 First 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 1CC formula:

1CC: p₁ (first prime), pβ‚‚ = 2p₁ + 1, p₃ = 2pβ‚‚ + 1, …
Cross-reference on Chainz Explorer
Circulating Supply:57,675,498 XPMΒ·at block #6,803,930 Β· updates every 60s
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