Block #306,173

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/11/2013, 9:33:56 PM · Difficulty 9.9938 · 6,504,994 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

545ed708c5af2716c1f5df69e32a442594567c94c619b43fd17aabaf0f1869ed

View on Chainz ↗

Height

#306,173

Difficulty

9.993831

Transactions

Size

969 B

Version

Bits

09fe6bb3

Nonce

317,418

Timestamp

12/11/2013, 9:33:56 PM

Confirmations

6,504,994

Mined by

⛏️ aRePAdwvoZJ4C5VxS7KoqqQtLWqKRah9vVTWnh

Merkle Root

81a84267df598b3eadf100d10689bfd0b668eb2042ed8775a5e0ae38e1988145

Transactions (1)

Coinbase81a84267df598b…e0ae38e1988145

1 in → 24 out10.0000 XPM879 B

AdwvoZJ4…h9vVTWnh AWQyM49v…zN9UeNMm APeshfYV…3PKcKMKH ARcqMJhp…RVLToQ6S AMAhFBm2…B1MTCAzU

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.

1.735 × 10⁹⁴(95-digit number)

17357102894505119238…53570282780246054401

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

1.735 × 10⁹⁴(95-digit number)

17357102894505119238…53570282780246054401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

3.471 × 10⁹⁴(95-digit number)

34714205789010238476…07140565560492108801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

6.942 × 10⁹⁴(95-digit number)

69428411578020476953…14281131120984217601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

1.388 × 10⁹⁵(96-digit number)

13885682315604095390…28562262241968435201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

2.777 × 10⁹⁵(96-digit number)

27771364631208190781…57124524483936870401

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

5.554 × 10⁹⁵(96-digit number)

55542729262416381563…14249048967873740801

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.110 × 10⁹⁶(97-digit number)

11108545852483276312…28498097935747481601

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

2.221 × 10⁹⁶(97-digit number)

22217091704966552625…56996195871494963201

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

4.443 × 10⁹⁶(97-digit number)

44434183409933105250…13992391742989926401

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 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

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 2CC formula:

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

Cross-reference on Chainz Explorer

Block #306,173

Cookie Preferences