Block #1,623,138

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/11/2016, 2:48:08 AM · Difficulty 10.5908 · 5,180,226 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

2f0d240a1f7e4a888eb2f6eb4d03336bf282baa05d75e4b7928d90a7e5bdbc1e

View on Chainz ↗

Height

#1,623,138

Difficulty

10.590784

Transactions

Size

575 B

Version

Bits

0a973d9d

Nonce

5,677,432

Timestamp

6/11/2016, 2:48:08 AM

Confirmations

5,180,226

Mined by

⛏️ P2SHAHMvf4XWF8Xxe7Q2vfYHzS6ywiqG6ePuX8

Merkle Root

97693cf0443d143a11089c72df25f91307405a350a2b95d3a915d97d201308ea

Transactions (2)

Coinbase3d087c3f5fefe0…caf0cd4e5f1902

1 in → 1 out8.9100 XPM110 B

AHMvf4XW…qG6ePuX8

a3a1b883d51f27…ead0eeb54e1f08

2 in → 2 out10048.8200 XPM375 B

AP2h3ch1…TLewSQUF AKnpVAke…AGbzyHFr

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.

6.578 × 10⁹³(94-digit number)

65785269516316273182…37018399380995389041

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

6.578 × 10⁹³(94-digit number)

65785269516316273182…37018399380995389041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.315 × 10⁹⁴(95-digit number)

13157053903263254636…74036798761990778081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

2.631 × 10⁹⁴(95-digit number)

26314107806526509272…48073597523981556161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

5.262 × 10⁹⁴(95-digit number)

52628215613053018545…96147195047963112321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.052 × 10⁹⁵(96-digit number)

10525643122610603709…92294390095926224641

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.105 × 10⁹⁵(96-digit number)

21051286245221207418…84588780191852449281

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

4.210 × 10⁹⁵(96-digit number)

42102572490442414836…69177560383704898561

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

8.420 × 10⁹⁵(96-digit number)

84205144980884829673…38355120767409797121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.684 × 10⁹⁶(97-digit number)

16841028996176965934…76710241534819594241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

3.368 × 10⁹⁶(97-digit number)

33682057992353931869…53420483069639188481

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