Block #140,224

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/29/2013, 12:38:53 PM · Difficulty 9.8327 · 6,654,561 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

08e54f2481e3635ec34df6f2fbf9ee5567f6dcf31fbf336757ff1e0efa6f54ad

View on Chainz ↗

Height

#140,224

Difficulty

9.832737

Transactions

Size

2.19 KB

Version

Bits

09d52e3e

Nonce

3,526

Timestamp

8/29/2013, 12:38:53 PM

Confirmations

6,654,561

Mined by

⛏️ P2SHAZXVzqHXGwmHdG5hzC1pZ1V5aoUmPamC9z

Merkle Root

12dbdb9c97c09d426cdd3f980d0269415b7d5fce67dce3421d44aaf7540f9eb7

Transactions (3)

Coinbase961c546158bab9…ae295d7fce5f6a

1 in → 1 out10.3600 XPM109 B

AZXVzqHX…UmPamC9z

d5c38080f6dc3e…4cdf63307fd43d

4 in → 2 out104.4279 XPM668 B

Abd1hnej…7EbdS3hM Ab7iXvjf…LnFwMDZn

d770a0641e5baf…14cf989b11ac99

9 in → 2 out50.8051 XPM1.34 KB

AQGqZchR…BMAoHard ARJ4HzmW…CSMnrfoe

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.

2.489 × 10⁹¹(92-digit number)

24896250315629809275…81544378048592471599

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

2.489 × 10⁹¹(92-digit number)

24896250315629809275…81544378048592471599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

4.979 × 10⁹¹(92-digit number)

49792500631259618551…63088756097184943199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

9.958 × 10⁹¹(92-digit number)

99585001262519237103…26177512194369886399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

1.991 × 10⁹²(93-digit number)

19917000252503847420…52355024388739772799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

3.983 × 10⁹²(93-digit number)

39834000505007694841…04710048777479545599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

7.966 × 10⁹²(93-digit number)

79668001010015389682…09420097554959091199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.593 × 10⁹³(94-digit number)

15933600202003077936…18840195109918182399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.186 × 10⁹³(94-digit number)

31867200404006155872…37680390219836364799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

6.373 × 10⁹³(94-digit number)

63734400808012311745…75360780439672729599

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