Block #437,553

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/10/2014, 9:28:08 AM · Difficulty 10.3573 · 6,374,670 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

e176cba6c79faee878118ed132cbbacc149725845caa0890b834cc1508c0bfac

View on Chainz ↗

Height

#437,553

Difficulty

10.357289

Transactions

Size

934 B

Version

Bits

0a5b7745

Nonce

2,929

Timestamp

3/10/2014, 9:28:08 AM

Confirmations

6,374,670

Mined by

⛏️ 1aSjAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

dd8bccc76cd8e28302a737566ca962efb9ad2522b0e4d9c60bd8b49ee85888db

Transactions (1)

Coinbasedd8bccc76cd8e2…d8b49ee85888db

1 in → 23 out9.3100 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGD4yZQw…hGzM2XAx AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6

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.

3.317 × 10⁹²(93-digit number)

33179662710003278610…12973323562434721209

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

3.317 × 10⁹²(93-digit number)

33179662710003278610…12973323562434721209

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.635 × 10⁹²(93-digit number)

66359325420006557220…25946647124869442419

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.327 × 10⁹³(94-digit number)

13271865084001311444…51893294249738884839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.654 × 10⁹³(94-digit number)

26543730168002622888…03786588499477769679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

5.308 × 10⁹³(94-digit number)

53087460336005245776…07573176998955539359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.061 × 10⁹⁴(95-digit number)

10617492067201049155…15146353997911078719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.123 × 10⁹⁴(95-digit number)

21234984134402098310…30292707995822157439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.246 × 10⁹⁴(95-digit number)

42469968268804196620…60585415991644314879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

8.493 × 10⁹⁴(95-digit number)

84939936537608393241…21170831983288629759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.698 × 10⁹⁵(96-digit number)

16987987307521678648…42341663966577259519

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 #437,553

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