Block #137,907

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/28/2013, 2:29:54 AM · Difficulty 9.8233 · 6,674,782 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

de9769fd1e1fb40afd8c6ff26cb850c031a2df23130e1f987cf55a7b3dcfe4c5

View on Chainz ↗

Height

#137,907

Difficulty

9.823281

Transactions

Size

887 B

Version

Bits

09d2c291

Nonce

213,204

Timestamp

8/28/2013, 2:29:54 AM

Confirmations

6,674,782

Mined by

⛏️ P2SHAQUowSVREMWB3cbTRasQEZNbSWDTfYbBoh

Merkle Root

b83776ae876aca5cdaf35ee58b4aa6c736ea99cba9e90c54b174b21ac12aacdf

Transactions (3)

Coinbasef2142a4527edac…723124596db8cc

1 in → 1 out10.3800 XPM109 B

AQUowSVR…DTfYbBoh

20dd9baf421703…5a09127c04a6ca

3 in → 2 out150.0250 XPM523 B

AX5Z1vWu…AganaQUZ Ac5HyAxi…8ztoPbo8

8d609ba5bb6f09…f90e0b2cc17eb9

1 in → 1 out10.4000 XPM159 B

AKN6pNCw…MeATKM2o

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.

1.103 × 10¹¹⁰(111-digit number)

11032506869301137233…99849069892794666539

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

1.103 × 10¹¹⁰(111-digit number)

11032506869301137233…99849069892794666539

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.206 × 10¹¹⁰(111-digit number)

22065013738602274466…99698139785589333079

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.413 × 10¹¹⁰(111-digit number)

44130027477204548933…99396279571178666159

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

8.826 × 10¹¹⁰(111-digit number)

88260054954409097866…98792559142357332319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.765 × 10¹¹¹(112-digit number)

17652010990881819573…97585118284714664639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.530 × 10¹¹¹(112-digit number)

35304021981763639146…95170236569429329279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.060 × 10¹¹¹(112-digit number)

70608043963527278293…90340473138858658559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.412 × 10¹¹²(113-digit number)

14121608792705455658…80680946277717317119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.824 × 10¹¹²(113-digit number)

28243217585410911317…61361892555434634239

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #137,907

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