Block #457,375

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/23/2014, 8:48:31 PM · Difficulty 10.4202 · 6,348,318 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e2aeee1f14f266635c11c8df7fee3dbfd4e7a7bc0ce66d3ed73d3f933f85aa61

View on Chainz ↗

Height

#457,375

Difficulty

10.420180

Transactions

Size

1.01 KB

Version

Bits

0a6b90e4

Nonce

813

Timestamp

3/23/2014, 8:48:31 PM

Confirmations

6,348,318

Mined by

⛏️ aSAFutDVqJywBDvDDzwUNgUinUiETJTJj6UF

Merkle Root

b7c50836a9b55bce3e863f1a21e63d1ac4b00538b2b246abfc65b36e6d1a1a87

Transactions (1)

Coinbaseb7c50836a9b55b…65b36e6d1a1a87

1 in → 26 out9.2000 XPM947 B

AFutDVqJ…TJTJj6UF ANNg88pG…ppn21sTe ATKK7iFz…wZm46KN1 ALqxX1WA…hsKjbnXn AQ8QAT3J…rCFKuVbR

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.

5.816 × 10⁹³(94-digit number)

58164251972032146807…83933647783755244799

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

5.816 × 10⁹³(94-digit number)

58164251972032146807…83933647783755244799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.163 × 10⁹⁴(95-digit number)

11632850394406429361…67867295567510489599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

2.326 × 10⁹⁴(95-digit number)

23265700788812858722…35734591135020979199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

4.653 × 10⁹⁴(95-digit number)

46531401577625717445…71469182270041958399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

9.306 × 10⁹⁴(95-digit number)

93062803155251434891…42938364540083916799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.861 × 10⁹⁵(96-digit number)

18612560631050286978…85876729080167833599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

3.722 × 10⁹⁵(96-digit number)

37225121262100573956…71753458160335667199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

7.445 × 10⁹⁵(96-digit number)

74450242524201147913…43506916320671334399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.489 × 10⁹⁶(97-digit number)

14890048504840229582…87013832641342668799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.978 × 10⁹⁶(97-digit number)

29780097009680459165…74027665282685337599

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