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Block #345,900

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 1/6/2014, 5:52:26 AM Β· Difficulty 10.2139 Β· 6,481,239 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e6da9fdddb3c032fa5708e5faf5848a444cff0bd82b904e7925fe663980fb117
View on Chainz β†—

Height

#345,900

Difficulty

10.213930

Transactions

2

Size

689 B

Version

2

Bits

0a36c423

Nonce

64,497

Timestamp

1/6/2014, 5:52:26 AM

Confirmations

6,481,239

Mined by

⛏️ P2SHAH81mMccfR5coBGmGi25n1JCzkB2JNrio2

Merkle Root

f44103f6bfc043c412f985fdc3f53535aa81456945af09c30b511983ae19af07
Transactions (2)
Coinbased507ef633722e6…eb2b4ca28ba800
1 in β†’ 1 out9.5800 XPM109 B
AH81mMcc…B2JNrio2
e4f7242ce98d52…ef7d4766dd5bbf
3 in β†’ 1 out0.5000 XPM489 B
APRQDa87…oXBY2irJ
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.

1.311 Γ— 10⁹⁷(98-digit number)
13119550910507654976…01879708854591999999
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
1.311 Γ— 10⁹⁷(98-digit number)
13119550910507654976…01879708854591999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.623 Γ— 10⁹⁷(98-digit number)
26239101821015309953…03759417709183999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.247 Γ— 10⁹⁷(98-digit number)
52478203642030619907…07518835418367999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.049 Γ— 10⁹⁸(99-digit number)
10495640728406123981…15037670836735999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.099 Γ— 10⁹⁸(99-digit number)
20991281456812247963…30075341673471999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.198 Γ— 10⁹⁸(99-digit number)
41982562913624495926…60150683346943999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.396 Γ— 10⁹⁸(99-digit number)
83965125827248991852…20301366693887999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.679 Γ— 10⁹⁹(100-digit number)
16793025165449798370…40602733387775999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.358 Γ— 10⁹⁹(100-digit number)
33586050330899596741…81205466775551999999
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
6.717 Γ— 10⁹⁹(100-digit number)
67172100661799193482…62410933551103999999
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:57,861,293 XPMΒ·at block #6,827,138 Β· updates every 60s
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