Block #440,561

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/12/2014, 12:28:21 PM · Difficulty 10.3527 · 6,369,058 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

35f825dfcf248a6bee66c3e17746e4288920eaf3c61c93e5a0b1d3e2e84aa165

View on Chainz ↗

Height

#440,561

Difficulty

10.352719

Transactions

Size

935 B

Version

Bits

0a5a4bd1

Nonce

327,648

Timestamp

3/12/2014, 12:28:21 PM

Confirmations

6,369,058

Mined by

⛏️ aSAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4b858f02fd9bcd62dd95f4cb0444967f0d83b5706940bd18ce417519a220167c

Transactions (1)

Coinbase4b858f02fd9bcd…417519a220167c

1 in → 23 out9.3200 XPM845 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.

2.175 × 10⁹⁵(96-digit number)

21750274305678480511…57334222702042313279

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

2.175 × 10⁹⁵(96-digit number)

21750274305678480511…57334222702042313279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.350 × 10⁹⁵(96-digit number)

43500548611356961022…14668445404084626559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

8.700 × 10⁹⁵(96-digit number)

87001097222713922045…29336890808169253119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.740 × 10⁹⁶(97-digit number)

17400219444542784409…58673781616338506239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.480 × 10⁹⁶(97-digit number)

34800438889085568818…17347563232677012479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

6.960 × 10⁹⁶(97-digit number)

69600877778171137636…34695126465354024959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.392 × 10⁹⁷(98-digit number)

13920175555634227527…69390252930708049919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.784 × 10⁹⁷(98-digit number)

27840351111268455054…38780505861416099839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

5.568 × 10⁹⁷(98-digit number)

55680702222536910109…77561011722832199679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.113 × 10⁹⁸(99-digit number)

11136140444507382021…55122023445664399359

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 #440,561

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