Block #1,088,195

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/3/2015, 12:11:14 PM · Difficulty 10.7507 · 5,711,332 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

c0f1c4368f1c160b67344501c1de3544669a6da24a257db32d4a993d1df33761

View on Chainz ↗

Height

#1,088,195

Difficulty

10.750735

Transactions

Size

243 B

Version

Bits

0ac03033

Nonce

56,957,358

Timestamp

6/3/2015, 12:11:14 PM

Confirmations

5,711,332

Mined by

⛏️ P2SHAPGBorYSVyrD2SpRvSHm34b51BQnZrTNSi

Merkle Root

46e8676c352d0ff6a77eb290a0ba1d8ad0e48549e0127e061215433028b3fe99

Transactions (1)

Coinbase46e8676c352d0f…15433028b3fe99

1 in → 2 out8.6400 XPM152 B

APGBorYS…QnZrTNSi ALPu3s2c…EJXLjVFh

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.

1.102 × 10⁹⁷(98-digit number)

11022571137169918620…95432663737238707201

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

1.102 × 10⁹⁷(98-digit number)

11022571137169918620…95432663737238707201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.204 × 10⁹⁷(98-digit number)

22045142274339837240…90865327474477414401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.409 × 10⁹⁷(98-digit number)

44090284548679674481…81730654948954828801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.818 × 10⁹⁷(98-digit number)

88180569097359348962…63461309897909657601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.763 × 10⁹⁸(99-digit number)

17636113819471869792…26922619795819315201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.527 × 10⁹⁸(99-digit number)

35272227638943739585…53845239591638630401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.054 × 10⁹⁸(99-digit number)

70544455277887479170…07690479183277260801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.410 × 10⁹⁹(100-digit number)

14108891055577495834…15380958366554521601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.821 × 10⁹⁹(100-digit number)

28217782111154991668…30761916733109043201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.643 × 10⁹⁹(100-digit number)

56435564222309983336…61523833466218086401

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