Block #372,071

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2014, 8:21:16 AM · Difficulty 10.4290 · 6,426,679 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

f81723a3f12ee8992458024109163616f27be633255642fbbdd945730c9a89b8

View on Chainz ↗

Height

#372,071

Difficulty

10.429034

Transactions

Size

934 B

Version

Bits

0a6dd52f

Nonce

12,541

Timestamp

1/23/2014, 8:21:16 AM

Confirmations

6,426,679

Mined by

⛏️ gaRuAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

4271e7c86e552615ed3fd1b3c3e5c7e751286dfe96990b48df28bfb89918d75e

Transactions (1)

Coinbase4271e7c86e5526…28bfb89918d75e

1 in → 23 out9.1800 XPM845 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6

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.

1.669 × 10⁹³(94-digit number)

16697380778126946931…95140877116192324099

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

1.669 × 10⁹³(94-digit number)

16697380778126946931…95140877116192324099

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.339 × 10⁹³(94-digit number)

33394761556253893863…90281754232384648199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.678 × 10⁹³(94-digit number)

66789523112507787726…80563508464769296399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.335 × 10⁹⁴(95-digit number)

13357904622501557545…61127016929538592799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.671 × 10⁹⁴(95-digit number)

26715809245003115090…22254033859077185599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

5.343 × 10⁹⁴(95-digit number)

53431618490006230181…44508067718154371199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.068 × 10⁹⁵(96-digit number)

10686323698001246036…89016135436308742399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

2.137 × 10⁹⁵(96-digit number)

21372647396002492072…78032270872617484799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

4.274 × 10⁹⁵(96-digit number)

42745294792004984145…56064541745234969599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

8.549 × 10⁹⁵(96-digit number)

85490589584009968290…12129083490469939199

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