Block #151,728

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 9/5/2013, 8:43:57 PM · Difficulty 9.8616 · 6,654,105 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

b8fb5229d1c6b82db027c52b98e8a9f4c594ecf06e5ce766f64a38668b174622

View on Chainz ↗

Height

#151,728

Difficulty

9.861613

Transactions

Size

470 B

Version

Bits

09dc92af

Nonce

127,293

Timestamp

9/5/2013, 8:43:57 PM

Confirmations

6,654,105

Mined by

⛏️ P2SHALi9bcAkC8ymfpqSkhEKevrr9dRfEfncQL

Merkle Root

b31f59ed8f5789ba31112f7df4775a4d23c4cd8fb61e2af84b50be5a4796961a

Transactions (2)

Coinbasec16311117b44ae…7848d3bed0409f

1 in → 1 out10.2800 XPM109 B

ALi9bcAk…RfEfncQL

db5e16b5a58efa…fd13b337118247

2 in → 1 out20.6400 XPM272 B

Abg9b4kX…im9CLs7g

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.

1.528 × 10⁹²(93-digit number)

15289050274983235226…25853540326957351859

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

1.528 × 10⁹²(93-digit number)

15289050274983235226…25853540326957351859

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

3.057 × 10⁹²(93-digit number)

30578100549966470453…51707080653914703719

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

6.115 × 10⁹²(93-digit number)

61156201099932940907…03414161307829407439

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.223 × 10⁹³(94-digit number)

12231240219986588181…06828322615658814879

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

2.446 × 10⁹³(94-digit number)

24462480439973176363…13656645231317629759

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

4.892 × 10⁹³(94-digit number)

48924960879946352726…27313290462635259519

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

9.784 × 10⁹³(94-digit number)

97849921759892705452…54626580925270519039

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.956 × 10⁹⁴(95-digit number)

19569984351978541090…09253161850541038079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.913 × 10⁹⁴(95-digit number)

39139968703957082180…18506323701082076159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

7.827 × 10⁹⁴(95-digit number)

78279937407914164361…37012647402164152319

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