Block #143,013

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 8/31/2013, 8:48:42 AM · Difficulty 9.8374 · 6,646,714 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

f19cf4684caf3e6949f512b42410841df4cc6c7a585e6ab69b345cb7a1c8c90c

View on Chainz ↗

Height

#143,013

Difficulty

9.837360

Transactions

Size

197 B

Version

Bits

09d65d33

Nonce

111,952

Timestamp

8/31/2013, 8:48:42 AM

Confirmations

6,646,714

Merkle Root

c7f339851ae85833db095a49b04cb61d2420999dcfeb23c9d46815070efd5655

Transactions (1)

Coinbasec7f339851ae858…6815070efd5655

1 in → 1 out10.3200 XPM109 B

AZv7gMUK…CbiASjGW

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.

5.183 × 10⁸⁹(90-digit number)

51837947881184402913…04520427091302233601

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

5.183 × 10⁸⁹(90-digit number)

51837947881184402913…04520427091302233601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.036 × 10⁹⁰(91-digit number)

10367589576236880582…09040854182604467201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.073 × 10⁹⁰(91-digit number)

20735179152473761165…18081708365208934401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

4.147 × 10⁹⁰(91-digit number)

41470358304947522330…36163416730417868801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

8.294 × 10⁹⁰(91-digit number)

82940716609895044661…72326833460835737601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.658 × 10⁹¹(92-digit number)

16588143321979008932…44653666921671475201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

3.317 × 10⁹¹(92-digit number)

33176286643958017864…89307333843342950401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

6.635 × 10⁹¹(92-digit number)

66352573287916035729…78614667686685900801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.327 × 10⁹²(93-digit number)

13270514657583207145…57229335373371801601

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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