Block #505,007

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/22/2014, 4:02:28 AM · Difficulty 10.8100 · 6,299,805 confirmations

1CC

Cunningham Chain of the First Kind

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

Block Header

Block Hash

641c918ff143beb0c8e181a67fbaaa6a731e76ce099149f9251fce75361b3f3a

View on Chainz ↗

Height

#505,007

Difficulty

10.810039

Transactions

Size

841 B

Version

Bits

0acf5eb0

Nonce

63,025,381

Timestamp

4/22/2014, 4:02:28 AM

Confirmations

6,299,805

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

bf19c03e5ff065b4b9d03c0af86cada9680296fa33c7e3e830ee71ed91c860a6

Transactions (2)

Coinbase8821a59cf591fe…567de935788aad

1 in → 1 out8.5500 XPM116 B

AbwWkWZt…kawDhufa

a8e2809c0551ae…32954274f9f691

4 in → 1 out156.9900 XPM635 B

AN2473CQ…ZTAKqBYu

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.

1.225 × 10⁹⁴(95-digit number)

12250598856638770386…33008768680365404699

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

1.225 × 10⁹⁴(95-digit number)

12250598856638770386…33008768680365404699

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^1 × origin − 1

2.450 × 10⁹⁴(95-digit number)

24501197713277540773…66017537360730809399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^2 × origin − 1

4.900 × 10⁹⁴(95-digit number)

49002395426555081546…32035074721461618799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^3 × origin − 1

9.800 × 10⁹⁴(95-digit number)

98004790853110163093…64070149442923237599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^4 × origin − 1

1.960 × 10⁹⁵(96-digit number)

19600958170622032618…28140298885846475199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^5 × origin − 1

3.920 × 10⁹⁵(96-digit number)

39201916341244065237…56280597771692950399

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^6 × origin − 1

7.840 × 10⁹⁵(96-digit number)

78403832682488130474…12561195543385900799

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^7 × origin − 1

1.568 × 10⁹⁶(97-digit number)

15680766536497626094…25122391086771801599

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^8 × origin − 1

3.136 × 10⁹⁶(97-digit number)

31361533072995252189…50244782173543603199

Verify on FactorDB ↗Wolfram Alpha ↗

×2+1 →

2^9 × origin − 1

6.272 × 10⁹⁶(97-digit number)

62723066145990504379…00489564347087206399

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