Block #573,119

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 6/2/2014, 12:40:40 PM · Difficulty 10.9666 · 6,222,640 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

78893b28856f22ea6590e920d26fdd5a16cf698765b8231fa55a1a3e1c394ddb

View on Chainz ↗

Height

#573,119

Difficulty

10.966592

Transactions

Size

629 B

Version

Bits

0af77295

Nonce

5,191

Timestamp

6/2/2014, 12:40:40 PM

Confirmations

6,222,640

Mined by

⛏️ aSpAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

88475d481d234aa375e7a904ddfb3d55a8b6c8681587fd4c9c4b57d8c12460fe

Transactions (1)

Coinbase88475d481d234a…4b57d8c12460fe

1 in → 14 out8.3000 XPM539 B

AQvZBsUo…hppgRZTJ AJzWx2VD…j4ZSMit5 AJtNW28X…Syb4Ph5j AdxPNkWD…ZMa9u34q AQyr8Lw3…hs4nt3Pn

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.

1.229 × 10⁹⁴(95-digit number)

12297209372039130261…88468985499610846241

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

1.229 × 10⁹⁴(95-digit number)

12297209372039130261…88468985499610846241

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.459 × 10⁹⁴(95-digit number)

24594418744078260522…76937970999221692481

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.918 × 10⁹⁴(95-digit number)

49188837488156521045…53875941998443384961

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

9.837 × 10⁹⁴(95-digit number)

98377674976313042091…07751883996886769921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.967 × 10⁹⁵(96-digit number)

19675534995262608418…15503767993773539841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.935 × 10⁹⁵(96-digit number)

39351069990525216836…31007535987547079681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

7.870 × 10⁹⁵(96-digit number)

78702139981050433673…62015071975094159361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.574 × 10⁹⁶(97-digit number)

15740427996210086734…24030143950188318721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

3.148 × 10⁹⁶(97-digit number)

31480855992420173469…48060287900376637441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

6.296 × 10⁹⁶(97-digit number)

62961711984840346938…96120575800753274881

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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …

Cross-reference on Chainz Explorer