Block #270,916

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/24/2013, 7:31:25 AM · Difficulty 9.9514 · 6,567,378 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

a0130162cdcd1dc35bca1e70bf272acffdd2e0b70b9c0b3a5d751bfda2f18b09

View on Chainz ↗

Height

#270,916

Difficulty

9.951399

Transactions

Size

2.04 KB

Version

Bits

09f38ee8

Nonce

39,009

Timestamp

11/24/2013, 7:31:25 AM

Confirmations

6,567,378

Mined by

⛏️ D"aRAdnG9gQ7MrBtC7Bjg1kQZzjdPFN9B7mA2p

Merkle Root

96add84ebf1a7b70cb978bddf7b70d20fa7b9134e2fb573c7723ceab76bb0ac0

Transactions (1)

Coinbase96add84ebf1a7b…23ceab76bb0ac0

1 in → 57 out10.0600 XPM1.95 KB

AdnG9gQ7…N9B7mA2p ARpndEmc…Hg792kEk ALxZyJxf…y1f3ARgv APeshfYV…3PKcKMKH AYQxpdCz…E9Wwwr6P

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.

4.332 × 10⁹²(93-digit number)

43322304031521601589…02534794862485597439

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

4.332 × 10⁹²(93-digit number)

43322304031521601589…02534794862485597439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

8.664 × 10⁹²(93-digit number)

86644608063043203178…05069589724971194879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.732 × 10⁹³(94-digit number)

17328921612608640635…10139179449942389759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

3.465 × 10⁹³(94-digit number)

34657843225217281271…20278358899884779519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

6.931 × 10⁹³(94-digit number)

69315686450434562542…40556717799769559039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

1.386 × 10⁹⁴(95-digit number)

13863137290086912508…81113435599539118079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

2.772 × 10⁹⁴(95-digit number)

27726274580173825017…62226871199078236159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

5.545 × 10⁹⁴(95-digit number)

55452549160347650034…24453742398156472319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

1.109 × 10⁹⁵(96-digit number)

11090509832069530006…48907484796312944639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

2.218 × 10⁹⁵(96-digit number)

22181019664139060013…97814969592625889279

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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …

Cross-reference on Chainz Explorer

Block #270,916

Cookie Preferences