Block #491,744

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/14/2014, 4:39:57 PM · Difficulty 10.6852 · 6,311,743 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

ec238f664adbe4c2579cbc1e32d4571d7a23e66e0e75a54a77569211ead1fecf

View on Chainz ↗

Height

#491,744

Difficulty

10.685159

Transactions

Size

901 B

Version

Bits

0aaf668f

Nonce

587,601

Timestamp

4/14/2014, 4:39:57 PM

Confirmations

6,311,743

Mined by

⛏️ aSLAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

bc3c6bda41000b16564b7b7edadcf2c1534c04f001662dff9504f2d72fb3283e

Transactions (1)

Coinbasebc3c6bda41000b…04f2d72fb3283e

1 in → 22 out8.7400 XPM811 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1

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.

3.995 × 10⁹⁴(95-digit number)

39955610670609750698…47688655403521105921

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

3.995 × 10⁹⁴(95-digit number)

39955610670609750698…47688655403521105921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.991 × 10⁹⁴(95-digit number)

79911221341219501397…95377310807042211841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.598 × 10⁹⁵(96-digit number)

15982244268243900279…90754621614084423681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.196 × 10⁹⁵(96-digit number)

31964488536487800559…81509243228168847361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.392 × 10⁹⁵(96-digit number)

63928977072975601118…63018486456337694721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.278 × 10⁹⁶(97-digit number)

12785795414595120223…26036972912675389441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.557 × 10⁹⁶(97-digit number)

25571590829190240447…52073945825350778881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.114 × 10⁹⁶(97-digit number)

51143181658380480894…04147891650701557761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.022 × 10⁹⁷(98-digit number)

10228636331676096178…08295783301403115521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.045 × 10⁹⁷(98-digit number)

20457272663352192357…16591566602806231041

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer