Block #55,953

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/17/2013, 4:54:25 AM · Difficulty 8.9455 · 6,735,040 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

3fbc0db4819462e3c1aa731f285de616bb6849dd7ca62a2851f311af0b206b42

View on Chainz ↗

Height

#55,953

Difficulty

8.945513

Transactions

Size

360 B

Version

Bits

08f20d23

Nonce

208

Timestamp

7/17/2013, 4:54:25 AM

Confirmations

6,735,040

Merkle Root

d0da19e882e10f342e84eec87dadff1e859eadbc4683a60349f94e763ce028be

Transactions (2)

Coinbasef84f79cdf11ce7…e4dc1fda525f92

1 in → 1 out12.4900 XPM110 B

APGtUz6m…8Tfy51aM

f6f8991d93b020…b75f95795038ce

1 in → 1 out12.5600 XPM159 B

AG43TCYA…UW1AUz7e

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.

8.495 × 10⁹⁷(98-digit number)

84957374758937197581…99903630496414825999

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

8.495 × 10⁹⁷(98-digit number)

84957374758937197581…99903630496414825999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

1.699 × 10⁹⁸(99-digit number)

16991474951787439516…99807260992829651999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

3.398 × 10⁹⁸(99-digit number)

33982949903574879032…99614521985659303999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

6.796 × 10⁹⁸(99-digit number)

67965899807149758065…99229043971318607999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.359 × 10⁹⁹(100-digit number)

13593179961429951613…98458087942637215999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

2.718 × 10⁹⁹(100-digit number)

27186359922859903226…96916175885274431999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

5.437 × 10⁹⁹(100-digit number)

54372719845719806452…93832351770548863999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.087 × 10¹⁰⁰(101-digit number)

10874543969143961290…87664703541097727999

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

2.174 × 10¹⁰⁰(101-digit number)

21749087938287922580…75329407082195455999

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