Block #448,967

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/18/2014, 7:28:19 AM · Difficulty 10.3657 · 6,354,594 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

4c086d7c4c8290447eac5b2beeeef06ad24302294286457bec6cb2b0d7f9dfaa

View on Chainz ↗

Height

#448,967

Difficulty

10.365658

Transactions

Size

833 B

Version

Bits

0a5d9bbb

Nonce

16,827

Timestamp

3/18/2014, 7:28:19 AM

Confirmations

6,354,594

Mined by

⛏️ aS'jAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3d64acc29e02a52a3346beead7c42914310e49e9cd40d482aecaa6e21b63c4f2

Transactions (1)

Coinbase3d64acc29e02a5…caa6e21b63c4f2

1 in → 20 out9.2900 XPM743 B

AQvZBsUo…hppgRZTJ AQ8QAT3J…rCFKuVbR 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.

2.353 × 10⁹⁴(95-digit number)

23535293929136835949…47338574900269065919

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

2.353 × 10⁹⁴(95-digit number)

23535293929136835949…47338574900269065919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.707 × 10⁹⁴(95-digit number)

47070587858273671899…94677149800538131839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.414 × 10⁹⁴(95-digit number)

94141175716547343798…89354299601076263679

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.882 × 10⁹⁵(96-digit number)

18828235143309468759…78708599202152527359

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.765 × 10⁹⁵(96-digit number)

37656470286618937519…57417198404305054719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.531 × 10⁹⁵(96-digit number)

75312940573237875038…14834396808610109439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.506 × 10⁹⁶(97-digit number)

15062588114647575007…29668793617220218879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.012 × 10⁹⁶(97-digit number)

30125176229295150015…59337587234440437759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.025 × 10⁹⁶(97-digit number)

60250352458590300030…18675174468880875519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.205 × 10⁹⁷(98-digit number)

12050070491718060006…37350348937761751039

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