Block #172,393

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/20/2013, 5:34:37 AM · Difficulty 9.8619 · 6,619,517 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

babf55b56e6593ce9e446fe9f76ded54de131533f3528d7b1ca1aab8728c1842

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Height

#172,393

Difficulty

9.861892

Transactions

Size

197 B

Version

Bits

09dca4ef

Nonce

14,902

Timestamp

9/20/2013, 5:34:37 AM

Confirmations

6,619,517

Merkle Root

c2108c937f649d349f0d755e039f84643f926a5ae553cc07e1d79bf336c25ee8

Transactions (1)

Coinbasec2108c937f649d…d79bf336c25ee8

1 in → 1 out10.2700 XPM109 B

AKhaGKFX…KjeAXtBv

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.

3.205 × 10⁹⁰(91-digit number)

32055566519011811897…89403887357156670001

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

3.205 × 10⁹⁰(91-digit number)

32055566519011811897…89403887357156670001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

6.411 × 10⁹⁰(91-digit number)

64111133038023623794…78807774714313340001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.282 × 10⁹¹(92-digit number)

12822226607604724758…57615549428626680001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.564 × 10⁹¹(92-digit number)

25644453215209449517…15231098857253360001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.128 × 10⁹¹(92-digit number)

51288906430418899035…30462197714506720001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.025 × 10⁹²(93-digit number)

10257781286083779807…60924395429013440001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.051 × 10⁹²(93-digit number)

20515562572167559614…21848790858026880001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.103 × 10⁹²(93-digit number)

41031125144335119228…43697581716053760001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

8.206 × 10⁹²(93-digit number)

82062250288670238456…87395163432107520001

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.641 × 10⁹³(94-digit number)

16412450057734047691…74790326864215040001

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