Block #389,183

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2014, 8:16:26 AM · Difficulty 10.4162 · 6,406,475 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

5f7dc833d7948ab2289db89c3c7dc652dc6e710e112ed9122be0a0518860be30

View on Chainz ↗

Height

#389,183

Difficulty

10.416167

Transactions

Size

866 B

Version

Bits

0a6a89e8

Nonce

618,601

Timestamp

2/4/2014, 8:16:26 AM

Confirmations

6,406,475

Mined by

⛏️ ?aRD3AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

2311e57a963b2984c8db4483031099eae92a2f76dbcd4a7413a86c309d578891

Transactions (1)

Coinbase2311e57a963b29…a86c309d578891

1 in → 21 out9.2000 XPM777 B

AQvZBsUo…hppgRZTJ AZV4TwxQ…8JnQqSoH Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 AczNP7Qa…nfcLAodi

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.

9.262 × 10⁹¹(92-digit number)

92627566649208187641…64806240910351878899

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

9.262 × 10⁹¹(92-digit number)

92627566649208187641…64806240910351878899

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.852 × 10⁹²(93-digit number)

18525513329841637528…29612481820703757799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.705 × 10⁹²(93-digit number)

37051026659683275056…59224963641407515599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

7.410 × 10⁹²(93-digit number)

74102053319366550113…18449927282815031199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.482 × 10⁹³(94-digit number)

14820410663873310022…36899854565630062399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.964 × 10⁹³(94-digit number)

29640821327746620045…73799709131260124799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.928 × 10⁹³(94-digit number)

59281642655493240090…47599418262520249599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.185 × 10⁹⁴(95-digit number)

11856328531098648018…95198836525040499199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.371 × 10⁹⁴(95-digit number)

23712657062197296036…90397673050080998399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

4.742 × 10⁹⁴(95-digit number)

47425314124394592072…80795346100161996799

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