Block #427,816

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/3/2014, 3:11:19 PM · Difficulty 10.3512 · 6,380,115 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5129c78ffa24f712492d4c934a12659aa511f43d1f781ff5ac16cc242fac9df5

View on Chainz ↗

Height

#427,816

Difficulty

10.351193

Transactions

Size

970 B

Version

Bits

0a59e7c8

Nonce

5,966

Timestamp

3/3/2014, 3:11:19 PM

Confirmations

6,380,115

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

8122a07bf3d3943f8b17675e2e9215046ee9ba9eb859f63dace022c02ed4fa65

Transactions (1)

Coinbase8122a07bf3d394…e022c02ed4fa65

1 in → 24 out9.3200 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.451 × 10⁹⁶(97-digit number)

14512132809736854077…28177599649234790399

Discovered Prime Numbers

p_k = 2^k × origin − 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.

origin − 1

1.451 × 10⁹⁶(97-digit number)

14512132809736854077…28177599649234790399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.902 × 10⁹⁶(97-digit number)

29024265619473708155…56355199298469580799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

5.804 × 10⁹⁶(97-digit number)

58048531238947416311…12710398596939161599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.160 × 10⁹⁷(98-digit number)

11609706247789483262…25420797193878323199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.321 × 10⁹⁷(98-digit number)

23219412495578966524…50841594387756646399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.643 × 10⁹⁷(98-digit number)

46438824991157933049…01683188775513292799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.287 × 10⁹⁷(98-digit number)

92877649982315866098…03366377551026585599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.857 × 10⁹⁸(99-digit number)

18575529996463173219…06732755102053171199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.715 × 10⁹⁸(99-digit number)

37151059992926346439…13465510204106342399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.430 × 10⁹⁸(99-digit number)

74302119985852692878…26931020408212684799

Verify on FactorDB ↗Wolfram Alpha ↗

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 — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

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 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #427,816

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