Block #196,396

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/6/2013, 11:18:26 AM · Difficulty 9.8808 · 6,607,644 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a9128bfa40bb99ad44c7968f9fb2a627217a92c8c801821f776d3a7ab5a0b731

View on Chainz ↗

Height

#196,396

Difficulty

9.880777

Transactions

Size

4.07 KB

Version

Bits

09e17a99

Nonce

1,164,818,622

Timestamp

10/6/2013, 11:18:26 AM

Confirmations

6,607,644

Mined by

⛏️ ,RQFIASLadjSZFoaHPeUQtDNzjovND2Nej8qyMq

Merkle Root

245f038b44c6bc812987a54225b807bad6cb85d07ac389744df80e2409758c40

Transactions (1)

Coinbase245f038b44c6bc…f80e2409758c40

1 in → 118 out10.1800 XPM3.98 KB

ASLadjSZ…Nej8qyMq ANx8jC5m…Do5qLVm4 AYup2sBS…rswv5GPw AeLXg8qu…77XGoqwh AGT9hnPx…C3sxd5B5

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.

3.664 × 10⁹³(94-digit number)

36647944347330578330…33748996318942528641

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

3.664 × 10⁹³(94-digit number)

36647944347330578330…33748996318942528641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

7.329 × 10⁹³(94-digit number)

73295888694661156660…67497992637885057281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.465 × 10⁹⁴(95-digit number)

14659177738932231332…34995985275770114561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.931 × 10⁹⁴(95-digit number)

29318355477864462664…69991970551540229121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

5.863 × 10⁹⁴(95-digit number)

58636710955728925328…39983941103080458241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.172 × 10⁹⁵(96-digit number)

11727342191145785065…79967882206160916481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.345 × 10⁹⁵(96-digit number)

23454684382291570131…59935764412321832961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

4.690 × 10⁹⁵(96-digit number)

46909368764583140262…19871528824643665921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

9.381 × 10⁹⁵(96-digit number)

93818737529166280525…39743057649287331841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.876 × 10⁹⁶(97-digit number)

18763747505833256105…79486115298574663681

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