Block #437,765

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/10/2014, 12:38:53 PM · Difficulty 10.3601 · 6,361,590 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

bd0b9d038f6685c730efc0fd0a8ef37e34fb0cd729fb7ce620f584cf65b0c158

View on Chainz ↗

Height

#437,765

Difficulty

10.360061

Transactions

Size

969 B

Version

Bits

0a5c2cf7

Nonce

2,760

Timestamp

3/10/2014, 12:38:53 PM

Confirmations

6,361,590

Mined by

⛏️ aSNAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

707706a3b83d040ee5a902a7a7434b41a6506e5453e829fcba7231e54807173d

Transactions (1)

Coinbase707706a3b83d04…7231e54807173d

1 in → 24 out9.3000 XPM879 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.

1.216 × 10⁹⁵(96-digit number)

12160382352556666522…85317966775415976319

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

1.216 × 10⁹⁵(96-digit number)

12160382352556666522…85317966775415976319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.432 × 10⁹⁵(96-digit number)

24320764705113333045…70635933550831952639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.864 × 10⁹⁵(96-digit number)

48641529410226666091…41271867101663905279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.728 × 10⁹⁵(96-digit number)

97283058820453332182…82543734203327810559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.945 × 10⁹⁶(97-digit number)

19456611764090666436…65087468406655621119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.891 × 10⁹⁶(97-digit number)

38913223528181332872…30174936813311242239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.782 × 10⁹⁶(97-digit number)

77826447056362665745…60349873626622484479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.556 × 10⁹⁷(98-digit number)

15565289411272533149…20699747253244968959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.113 × 10⁹⁷(98-digit number)

31130578822545066298…41399494506489937919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.226 × 10⁹⁷(98-digit number)

62261157645090132596…82798989012979875839

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