Block #506,973

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/23/2014, 10:23:30 AM · Difficulty 10.8157 · 6,285,852 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

e8eadc68114ededa6a4e5ae6cc67d174152d88b7202c7815164de0db4506e5df

View on Chainz ↗

Height

#506,973

Difficulty

10.815695

Transactions

Size

800 B

Version

Bits

0ad0d164

Nonce

13,075

Timestamp

4/23/2014, 10:23:30 AM

Confirmations

6,285,852

Merkle Root

279b1f84f2ec4d288ff6771f6fccec0ba7234819b2b239fa9443a7621b4db3e6

Transactions (1)

Coinbase279b1f84f2ec4d…43a7621b4db3e6

1 in → 19 out8.5300 XPM709 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.

2.114 × 10⁹⁶(97-digit number)

21148501930590581438…52225629900619294721

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

2.114 × 10⁹⁶(97-digit number)

21148501930590581438…52225629900619294721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.229 × 10⁹⁶(97-digit number)

42297003861181162876…04451259801238589441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

8.459 × 10⁹⁶(97-digit number)

84594007722362325753…08902519602477178881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.691 × 10⁹⁷(98-digit number)

16918801544472465150…17805039204954357761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.383 × 10⁹⁷(98-digit number)

33837603088944930301…35610078409908715521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

6.767 × 10⁹⁷(98-digit number)

67675206177889860602…71220156819817431041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.353 × 10⁹⁸(99-digit number)

13535041235577972120…42440313639634862081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.707 × 10⁹⁸(99-digit number)

27070082471155944241…84880627279269724161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

5.414 × 10⁹⁸(99-digit number)

54140164942311888482…69761254558539448321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.082 × 10⁹⁹(100-digit number)

10828032988462377696…39522509117078896641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

2.165 × 10⁹⁹(100-digit number)

21656065976924755392…79045018234157793281

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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