Block #1,475,445

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/28/2016, 11:59:24 AM · Difficulty 10.6915 · 5,368,375 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

b79a029eeae5db1761b0e685142017b35af621d80fdd81f0ac224818bd222562

View on Chainz ↗

Height

#1,475,445

Difficulty

10.691544

Transactions

Size

243 B

Version

Bits

0ab1090f

Nonce

168,255,565

Timestamp

2/28/2016, 11:59:24 AM

Confirmations

5,368,375

Mined by

⛏️ P2SHAdwKJkgSub5gUckyBUnSUJCm23L2zsc2ej

Merkle Root

3d653519b62c808fdb073c67ea2a73bbb8766a6675cd73bfe65be811dab3e66e

Transactions (1)

Coinbase3d653519b62c80…5be811dab3e66e

1 in → 2 out8.7300 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.

9.562 × 10⁹⁷(98-digit number)

95623028064345530236…63103252384164423681

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

9.562 × 10⁹⁷(98-digit number)

95623028064345530236…63103252384164423681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.912 × 10⁹⁸(99-digit number)

19124605612869106047…26206504768328847361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.824 × 10⁹⁸(99-digit number)

38249211225738212094…52413009536657694721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

7.649 × 10⁹⁸(99-digit number)

76498422451476424188…04826019073315389441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.529 × 10⁹⁹(100-digit number)

15299684490295284837…09652038146630778881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.059 × 10⁹⁹(100-digit number)

30599368980590569675…19304076293261557761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.119 × 10⁹⁹(100-digit number)

61198737961181139351…38608152586523115521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.223 × 10¹⁰⁰(101-digit number)

12239747592236227870…77216305173046231041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.447 × 10¹⁰⁰(101-digit number)

24479495184472455740…54432610346092462081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

4.895 × 10¹⁰⁰(101-digit number)

48958990368944911480…08865220692184924161

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 #1,475,445

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