Block #1,474,562

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/27/2016, 9:27:56 PM · Difficulty 10.6908 · 5,368,121 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

29749ddd3a1b26e19de5475d5be8b91de55e1e4d957fda29952fe7d4a51edc2e

View on Chainz ↗

Height

#1,474,562

Difficulty

10.690762

Transactions

Size

243 B

Version

Bits

0ab0d5cb

Nonce

1,234,458,473

Timestamp

2/27/2016, 9:27:56 PM

Confirmations

5,368,121

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

eb972458d76bb718be394b82c605c2f55362bb73f44d0668490103fd2de71d2a

Transactions (1)

Coinbaseeb972458d76bb7…0103fd2de71d2a

1 in → 2 out8.7400 XPM152 B

AdwKJkgS…L2zsc2ej 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.

4.245 × 10⁹⁶(97-digit number)

42451947720472218442…17854821824184633121

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

4.245 × 10⁹⁶(97-digit number)

42451947720472218442…17854821824184633121

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

8.490 × 10⁹⁶(97-digit number)

84903895440944436885…35709643648369266241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.698 × 10⁹⁷(98-digit number)

16980779088188887377…71419287296738532481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

3.396 × 10⁹⁷(98-digit number)

33961558176377774754…42838574593477064961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

6.792 × 10⁹⁷(98-digit number)

67923116352755549508…85677149186954129921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

1.358 × 10⁹⁸(99-digit number)

13584623270551109901…71354298373908259841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

2.716 × 10⁹⁸(99-digit number)

27169246541102219803…42708596747816519681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

5.433 × 10⁹⁸(99-digit number)

54338493082204439606…85417193495633039361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

1.086 × 10⁹⁹(100-digit number)

10867698616440887921…70834386991266078721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

2.173 × 10⁹⁹(100-digit number)

21735397232881775842…41668773982532157441

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

Block #1,474,562

Cookie Preferences