Block #54,938

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/16/2013, 11:06:23 PM · Difficulty 8.9378 · 6,734,810 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

29f3ff84e9ac472672f7b1f14fac39817650f68fdae43239463e880ecd07a3e7

View on Chainz ↗

Height

#54,938

Difficulty

8.937762

Transactions

Size

871 B

Version

Bits

08f01132

Nonce

119

Timestamp

7/16/2013, 11:06:23 PM

Confirmations

6,734,810

Merkle Root

38f3eaf7ccc2c07e53ceea343ae096be9ac870395262aa7b822a8d0fae7d2002

Transactions (2)

Coinbase1ad32c226c4e4d…8f0a05206e349d

1 in → 1 out12.5100 XPM110 B

AVkQsqkc…NnZ8vi1V

f53888f21b0880…a903bc6466acb9

4 in → 2 out511.3017 XPM669 B

AdgYRRhn…w7mNYBU7 ANwp4cEC…fLEo84T1

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.

3.061 × 10⁹⁸(99-digit number)

30616356392880177088…29673007674848209319

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

3.061 × 10⁹⁸(99-digit number)

30616356392880177088…29673007674848209319

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

6.123 × 10⁹⁸(99-digit number)

61232712785760354176…59346015349696418639

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

1.224 × 10⁹⁹(100-digit number)

12246542557152070835…18692030699392837279

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

2.449 × 10⁹⁹(100-digit number)

24493085114304141670…37384061398785674559

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

4.898 × 10⁹⁹(100-digit number)

48986170228608283340…74768122797571349119

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

9.797 × 10⁹⁹(100-digit number)

97972340457216566681…49536245595142698239

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

1.959 × 10¹⁰⁰(101-digit number)

19594468091443313336…99072491190285396479

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

3.918 × 10¹⁰⁰(101-digit number)

39188936182886626672…98144982380570792959

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

7.837 × 10¹⁰⁰(101-digit number)

78377872365773253345…96289964761141585919

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