Block #370,890

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/22/2014, 11:30:40 AM · Difficulty 10.4365 · 6,423,919 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

136f7d71213dcba94066dfa0102447544f002e10364f7aa97393a22e871b7e29

View on Chainz ↗

Height

#370,890

Difficulty

10.436547

Transactions

Size

229 B

Version

Bits

0a6fc190

Nonce

72,553

Timestamp

1/22/2014, 11:30:40 AM

Confirmations

6,423,919

Mined by

⛏️ P2SHARmAMwyuAi8euPwQcDptyGopF9P7Kn74ZT

Merkle Root

0635a52de67a5c243b7ec802a2168e5e834c03c67c45ed19578d0767ba2d765f

Transactions (1)

Coinbase0635a52de67a5c…8d0767ba2d765f

1 in → 2 out9.1700 XPM136 B

ARmAMwyu…P7Kn74ZT AU6kq4CL…dQBLvxLp

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.

1.105 × 10¹⁰³(104-digit number)

11057418161836973258…42142260447912053759

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

1.105 × 10¹⁰³(104-digit number)

11057418161836973258…42142260447912053759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.211 × 10¹⁰³(104-digit number)

22114836323673946517…84284520895824107519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.422 × 10¹⁰³(104-digit number)

44229672647347893035…68569041791648215039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.845 × 10¹⁰³(104-digit number)

88459345294695786071…37138083583296430079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.769 × 10¹⁰⁴(105-digit number)

17691869058939157214…74276167166592860159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.538 × 10¹⁰⁴(105-digit number)

35383738117878314428…48552334333185720319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.076 × 10¹⁰⁴(105-digit number)

70767476235756628856…97104668666371440639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.415 × 10¹⁰⁵(106-digit number)

14153495247151325771…94209337332742881279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.830 × 10¹⁰⁵(106-digit number)

28306990494302651542…88418674665485762559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

5.661 × 10¹⁰⁵(106-digit number)

56613980988605303085…76837349330971525119

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