Block #496,311

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/17/2014, 12:56:59 AM · Difficulty 10.7519 · 6,295,263 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

5312ec3dea8aa247ae140330f334db6b278a01690ca67aee4b51fbb9123f112d

View on Chainz ↗

Height

#496,311

Difficulty

10.751949

Transactions

Size

832 B

Version

Bits

0ac07fb3

Nonce

1,279

Timestamp

4/17/2014, 12:56:59 AM

Confirmations

6,295,263

Merkle Root

b0612cebdbcd35a5363ff2def313c43385c173a13d65a2eacec877ea4843e44a

Transactions (1)

Coinbaseb0612cebdbcd35…c877ea4843e44a

1 in → 20 out8.6400 XPM743 B

AQvZBsUo…hppgRZTJ ANNg88pG…ppn21sTe AWMrD5hP…ZwsoxvZ3 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.

8.900 × 10⁹²(93-digit number)

89008370785734448293…74775610280670454401

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

8.900 × 10⁹²(93-digit number)

89008370785734448293…74775610280670454401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.780 × 10⁹³(94-digit number)

17801674157146889658…49551220561340908801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.560 × 10⁹³(94-digit number)

35603348314293779317…99102441122681817601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.120 × 10⁹³(94-digit number)

71206696628587558634…98204882245363635201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.424 × 10⁹⁴(95-digit number)

14241339325717511726…96409764490727270401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.848 × 10⁹⁴(95-digit number)

28482678651435023453…92819528981454540801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.696 × 10⁹⁴(95-digit number)

56965357302870046907…85639057962909081601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.139 × 10⁹⁵(96-digit number)

11393071460574009381…71278115925818163201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.278 × 10⁹⁵(96-digit number)

22786142921148018763…42556231851636326401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.557 × 10⁹⁵(96-digit number)

45572285842296037526…85112463703272652801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

9.114 × 10⁹⁵(96-digit number)

91144571684592075052…70224927406545305601

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