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Block #331,155

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/27/2013, 4:30:44 AM Β· Difficulty 10.1665 Β· 6,465,103 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ea86be07ef9eb8b526791788caf44552db6add878eb4b7f843a17dabfacd58f4
View on Chainz β†—

Height

#331,155

Difficulty

10.166501

Transactions

2

Size

344 B

Version

2

Bits

0a2a9fca

Nonce

229,841

Timestamp

12/27/2013, 4:30:44 AM

Confirmations

6,465,103

Mined by

⛏️ aRD"vAbMAHMS8edmSw9jhkJ2fCCZzvKMwEzMSoj

Merkle Root

57e8c283c10ae6ad49f34f8eb0ab3ce4f88b237643c4dded67580d4b5d4e79c3
Transactions (2)
Coinbase9c7995ffc827bb…d3f199ada56553
1 in β†’ 1 out9.6600 XPM97 B
AbMAHMS8…MwEzMSoj
2f4419903f4e28…fa112a95985ee7
1 in β†’ 1 out9.8479 XPM158 B
AFqYA8s7…xpFKHo7K
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.

1.444 Γ— 10⁹²(93-digit number)
14444959299365548643…28390657437009127679
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
1.444 Γ— 10⁹²(93-digit number)
14444959299365548643…28390657437009127679
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.888 Γ— 10⁹²(93-digit number)
28889918598731097287…56781314874018255359
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.777 Γ— 10⁹²(93-digit number)
57779837197462194574…13562629748036510719
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.155 Γ— 10⁹³(94-digit number)
11555967439492438914…27125259496073021439
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.311 Γ— 10⁹³(94-digit number)
23111934878984877829…54250518992146042879
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.622 Γ— 10⁹³(94-digit number)
46223869757969755659…08501037984292085759
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
9.244 Γ— 10⁹³(94-digit number)
92447739515939511319…17002075968584171519
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.848 Γ— 10⁹⁴(95-digit number)
18489547903187902263…34004151937168343039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.697 Γ— 10⁹⁴(95-digit number)
36979095806375804527…68008303874336686079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.395 Γ— 10⁹⁴(95-digit number)
73958191612751609055…36016607748673372159
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:57,614,062 XPMΒ·at block #6,796,257 Β· updates every 60s
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