Block #475,544

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/5/2014, 7:19:43 AM · Difficulty 10.4589 · 6,332,313 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

99091f440ec2d9eacb3fd65af25e6b40b669ee0fbbbe31d143068c8374c02927

View on Chainz ↗

Height

#475,544

Difficulty

10.458863

Transactions

Size

900 B

Version

Bits

0a75780a

Nonce

10,436

Timestamp

4/5/2014, 7:19:43 AM

Confirmations

6,332,313

Mined by

⛏️ AAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

a59129a6872f7266329c59ce0aea2a77fec6386e2b15136e67208edc0a30e0e5

Transactions (1)

Coinbasea59129a6872f72…208edc0a30e0e5

1 in → 22 out9.1300 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AMW1p9oT…2TzdaZxH ATp4jJhs…TbSgR8Qb AUzEPJFG…kYkA5U9V

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.

1.236 × 10⁹²(93-digit number)

12367656087250783849…47358770713493211319

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

1.236 × 10⁹²(93-digit number)

12367656087250783849…47358770713493211319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.473 × 10⁹²(93-digit number)

24735312174501567699…94717541426986422639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.947 × 10⁹²(93-digit number)

49470624349003135399…89435082853972845279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.894 × 10⁹²(93-digit number)

98941248698006270799…78870165707945690559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.978 × 10⁹³(94-digit number)

19788249739601254159…57740331415891381119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.957 × 10⁹³(94-digit number)

39576499479202508319…15480662831782762239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.915 × 10⁹³(94-digit number)

79152998958405016639…30961325663565524479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.583 × 10⁹⁴(95-digit number)

15830599791681003327…61922651327131048959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.166 × 10⁹⁴(95-digit number)

31661199583362006655…23845302654262097919

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.332 × 10⁹⁴(95-digit number)

63322399166724013311…47690605308524195839

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 #475,544

Cookie Preferences