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Block #1,371,826

1CCLength 10β˜…β˜…β˜†β˜†β˜†

Cunningham Chain of the First Kind Β· Discovered 12/16/2015, 6:44:37 PM Β· Difficulty 10.8103 Β· 5,466,392 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9a53c3fdbdd7b46eb293863746c80d8270f6fa58965593d840d094335d15a023
View on Chainz β†—

Height

#1,371,826

Difficulty

10.810279

Transactions

1

Size

200 B

Version

2

Bits

0acf6e70

Nonce

622,448,104

Timestamp

12/16/2015, 6:44:37 PM

Confirmations

5,466,392

Mined by

⛏️ P2SHAQr7vWrsz6tqUsYy7j62HKh6LmUkrGrJFt

Merkle Root

ef1fe05fae8965dbf8ce50ab5d2811eae6f34a8822e41dac6e6cce7e3c0a78ab
Transactions (1)
Coinbaseef1fe05fae8965…6cce7e3c0a78ab
1 in β†’ 1 out8.5400 XPM110 B
AQr7vWrs…UkrGrJFt
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.

2.148 Γ— 10⁹⁴(95-digit number)
21480740121890147100…55660032144754912399
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
2.148 Γ— 10⁹⁴(95-digit number)
21480740121890147100…55660032144754912399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
2
2^1 Γ— origin βˆ’ 1
4.296 Γ— 10⁹⁴(95-digit number)
42961480243780294200…11320064289509824799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
3
2^2 Γ— origin βˆ’ 1
8.592 Γ— 10⁹⁴(95-digit number)
85922960487560588401…22640128579019649599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
4
2^3 Γ— origin βˆ’ 1
1.718 Γ— 10⁹⁡(96-digit number)
17184592097512117680…45280257158039299199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
5
2^4 Γ— origin βˆ’ 1
3.436 Γ— 10⁹⁡(96-digit number)
34369184195024235360…90560514316078598399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
6
2^5 Γ— origin βˆ’ 1
6.873 Γ— 10⁹⁡(96-digit number)
68738368390048470720…81121028632157196799
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
7
2^6 Γ— origin βˆ’ 1
1.374 Γ— 10⁹⁢(97-digit number)
13747673678009694144…62242057264314393599
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
8
2^7 Γ— origin βˆ’ 1
2.749 Γ— 10⁹⁢(97-digit number)
27495347356019388288…24484114528628787199
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
9
2^8 Γ— origin βˆ’ 1
5.499 Γ— 10⁹⁢(97-digit number)
54990694712038776576…48968229057257574399
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2+1 β†’
10
2^9 Γ— origin βˆ’ 1
1.099 Γ— 10⁹⁷(98-digit number)
10998138942407755315…97936458114515148799
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:57,950,018 XPMΒ·at block #6,838,217 Β· updates every 60s
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