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Block #312,646

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/15/2013, 3:03:20 AM Β· Difficulty 9.9959 Β· 6,496,608 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aae311c2cb90e5e48a4904dad24ef7f51210541e56714df98977cd8aa0df2598
View on Chainz β†—

Height

#312,646

Difficulty

9.995872

Transactions

1

Size

200 B

Version

2

Bits

09fef17a

Nonce

84,500

Timestamp

12/15/2013, 3:03:20 AM

Confirmations

6,496,608

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

9662f0afcf058efa28925ad51adb7a06c1543a103bf2b30ec497008bf3f28e58
Transactions (1)
Coinbase9662f0afcf058e…97008bf3f28e58
1 in β†’ 1 out9.9900 XPM110 B
AeKNrjNj…1NEq95Ta
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.

4.519 Γ— 10⁹⁡(96-digit number)
45198314097297361289…77056485503099863039
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
4.519 Γ— 10⁹⁡(96-digit number)
45198314097297361289…77056485503099863039
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
9.039 Γ— 10⁹⁡(96-digit number)
90396628194594722579…54112971006199726079
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
1.807 Γ— 10⁹⁢(97-digit number)
18079325638918944515…08225942012399452159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
3.615 Γ— 10⁹⁢(97-digit number)
36158651277837889031…16451884024798904319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
7.231 Γ— 10⁹⁢(97-digit number)
72317302555675778063…32903768049597808639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
1.446 Γ— 10⁹⁷(98-digit number)
14463460511135155612…65807536099195617279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
2.892 Γ— 10⁹⁷(98-digit number)
28926921022270311225…31615072198391234559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
5.785 Γ— 10⁹⁷(98-digit number)
57853842044540622450…63230144396782469119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
1.157 Γ— 10⁹⁸(99-digit number)
11570768408908124490…26460288793564938239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
2.314 Γ— 10⁹⁸(99-digit number)
23141536817816248980…52920577587129876479
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:57,718,098 XPMΒ·at block #6,809,253 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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