Block #179,174

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/24/2013, 9:43:02 PM · Difficulty 9.8637 · 6,626,894 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2bd105ba20da25ce9d5c1a3a2b06941f2ff5ec2b1c02a646b206c625c8ceb9f3

View on Chainz ↗

Height

#179,174

Difficulty

9.863715

Transactions

Size

560 B

Version

Bits

09dd1c69

Nonce

1,164,935,543

Timestamp

9/24/2013, 9:43:02 PM

Confirmations

6,626,894

Mined by

⛏️ RBAV4rziFj7Cxd8XM5wH4Y1cst3cQhTLsLyZ

Merkle Root

c4e438ad5b7950c89320abf2ee8ba8da3ca2997971d806c781a8aaa5df62df4c

Transactions (1)

Coinbasec4e438ad5b7950…a8aaa5df62df4c

1 in → 12 out10.2600 XPM470 B

AV4rziFj…QhTLsLyZ ANscdPEm…b8DYdwDD AeckU1Kq…a9chH61d AFq51nP4…FqYfXapg AR7hUyNW…iuooRCti

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.

2.346 × 10⁹³(94-digit number)

23465555344901302819…48942713661743924201

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

2.346 × 10⁹³(94-digit number)

23465555344901302819…48942713661743924201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

4.693 × 10⁹³(94-digit number)

46931110689802605638…97885427323487848401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

9.386 × 10⁹³(94-digit number)

93862221379605211276…95770854646975696801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.877 × 10⁹⁴(95-digit number)

18772444275921042255…91541709293951393601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

3.754 × 10⁹⁴(95-digit number)

37544888551842084510…83083418587902787201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

7.508 × 10⁹⁴(95-digit number)

75089777103684169020…66166837175805574401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.501 × 10⁹⁵(96-digit number)

15017955420736833804…32333674351611148801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.003 × 10⁹⁵(96-digit number)

30035910841473667608…64667348703222297601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.007 × 10⁹⁵(96-digit number)

60071821682947335216…29334697406444595201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.201 × 10⁹⁶(97-digit number)

12014364336589467043…58669394812889190401

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