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Block #2,566,678

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 3/15/2018, 7:02:39 AM Β· Difficulty 10.9936 Β· 4,278,549 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
75abd67b1a2101c458539ada0e42b4b44b6e05c9324b5b5bde01d4028582e748
View on Chainz β†—

Height

#2,566,678

Difficulty

10.993582

Transactions

1

Size

199 B

Version

2

Bits

0afe5b63

Nonce

980,987,580

Timestamp

3/15/2018, 7:02:39 AM

Confirmations

4,278,549

Mined by

⛏️ P2SHAGsrKyawAhJiteSFFYR9haa1A38tyEFbke

Merkle Root

94a57fe0bc72c4e1de3c1aea922f5af2ffae2acd7ee3622b9a00a57167e7f5f1
Transactions (1)
Coinbase94a57fe0bc72c4…00a57167e7f5f1
1 in β†’ 1 out8.2600 XPM109 B
AGsrKyaw…8tyEFbke
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.

1.378 Γ— 10⁹⁡(96-digit number)
13782335770829060986…22688303643645764159
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
1.378 Γ— 10⁹⁡(96-digit number)
13782335770829060986…22688303643645764159
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
2.756 Γ— 10⁹⁡(96-digit number)
27564671541658121973…45376607287291528319
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
5.512 Γ— 10⁹⁡(96-digit number)
55129343083316243947…90753214574583056639
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.102 Γ— 10⁹⁢(97-digit number)
11025868616663248789…81506429149166113279
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
2.205 Γ— 10⁹⁢(97-digit number)
22051737233326497579…63012858298332226559
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
4.410 Γ— 10⁹⁢(97-digit number)
44103474466652995158…26025716596664453119
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
8.820 Γ— 10⁹⁢(97-digit number)
88206948933305990316…52051433193328906239
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
1.764 Γ— 10⁹⁷(98-digit number)
17641389786661198063…04102866386657812479
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
3.528 Γ— 10⁹⁷(98-digit number)
35282779573322396126…08205732773315624959
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
7.056 Γ— 10⁹⁷(98-digit number)
70565559146644792253…16411465546631249919
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:58,006,248 XPMΒ·at block #6,845,226 Β· updates every 60s
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