Block #497,342

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/17/2014, 1:17:07 PM · Difficulty 10.7663 · 6,301,938 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

6dc8efc5ed21fc18be9b4754bab3e5dd3e989c5a362122785a35e9b4c18a3a0f

View on Chainz ↗

Height

#497,342

Difficulty

10.766291

Transactions

Size

832 B

Version

Bits

0ac42bad

Nonce

10,127

Timestamp

4/17/2014, 1:17:07 PM

Confirmations

6,301,938

Mined by

⛏️ aSOAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4195e8a514ed44f951d9938d84c7e178c3088dc07ef4026b8c3700210eedba77

Transactions (1)

Coinbase4195e8a514ed44…3700210eedba77

1 in → 20 out8.6100 XPM742 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AdxPNkWD…ZMa9u34q ATKK7iFz…wZm46KN1 AJtNW28X…Syb4Ph5j

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.

3.836 × 10⁹³(94-digit number)

38363257330766969168…52197336811965424639

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

3.836 × 10⁹³(94-digit number)

38363257330766969168…52197336811965424639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

7.672 × 10⁹³(94-digit number)

76726514661533938337…04394673623930849279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.534 × 10⁹⁴(95-digit number)

15345302932306787667…08789347247861698559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.069 × 10⁹⁴(95-digit number)

30690605864613575334…17578694495723397119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.138 × 10⁹⁴(95-digit number)

61381211729227150669…35157388991446794239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.227 × 10⁹⁵(96-digit number)

12276242345845430133…70314777982893588479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.455 × 10⁹⁵(96-digit number)

24552484691690860267…40629555965787176959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

4.910 × 10⁹⁵(96-digit number)

49104969383381720535…81259111931574353919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

9.820 × 10⁹⁵(96-digit number)

98209938766763441071…62518223863148707839

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

1.964 × 10⁹⁶(97-digit number)

19641987753352688214…25036447726297415679

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