Block #215,714

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/18/2013, 6:48:01 AM · Difficulty 9.9255 · 6,579,886 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2c95e59b2ff1d2bbcabc123700fb2dc75f4aea70d8f1962e893891db6ec39beb

View on Chainz ↗

Height

#215,714

Difficulty

9.925476

Transactions

Size

5.56 KB

Version

Bits

09ecebff

Nonce

79,426

Timestamp

10/18/2013, 6:48:01 AM

Confirmations

6,579,886

Mined by

⛏️ JR`ASGXhVnpHDqZQvfNr3qxQTF9hZgHNxHQYB

Merkle Root

318ed29278bc7ab115e2f2249412280753647714c045c5d61aab8663101b453e

Transactions (1)

Coinbase318ed29278bc7a…ab8663101b453e

1 in → 163 out10.0800 XPM5.47 KB

ASGXhVnp…gHNxHQYB APvpz12N…NjdsxTYA ANWEGnpn…gB9ZUftb Aa6xA9KK…o7woWzPm AJWc12T9…gdZnUvYf

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.

2.815 × 10⁹⁵(96-digit number)

28150018046698914813…94045362021355398401

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

2.815 × 10⁹⁵(96-digit number)

28150018046698914813…94045362021355398401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.630 × 10⁹⁵(96-digit number)

56300036093397829626…88090724042710796801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.126 × 10⁹⁶(97-digit number)

11260007218679565925…76181448085421593601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.252 × 10⁹⁶(97-digit number)

22520014437359131850…52362896170843187201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.504 × 10⁹⁶(97-digit number)

45040028874718263701…04725792341686374401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

9.008 × 10⁹⁶(97-digit number)

90080057749436527402…09451584683372748801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.801 × 10⁹⁷(98-digit number)

18016011549887305480…18903169366745497601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.603 × 10⁹⁷(98-digit number)

36032023099774610960…37806338733490995201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

7.206 × 10⁹⁷(98-digit number)

72064046199549221921…75612677466981990401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

1.441 × 10⁹⁸(99-digit number)

14412809239909844384…51225354933963980801

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