Block #73,914

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 7/21/2013, 8:28:16 AM · Difficulty 8.9952 · 6,721,549 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

272509b65b8b89d84acda07178ff3766593b51f033c139763dced4d6407dad4a

View on Chainz ↗

Height

#73,914

Difficulty

8.995153

Transactions

Size

206 B

Version

Bits

08fec260

Nonce

691

Timestamp

7/21/2013, 8:28:16 AM

Confirmations

6,721,549

Mined by

⛏️ P2SHARjfZHEf6BDcoYj5duXJT9ZYUm4npnTQw4

Merkle Root

3bb5c5a41f3e6f97a8e063cb59dda5365267f477c8ca3c752565f190d93663d0

Transactions (1)

Coinbase3bb5c5a41f3e6f…65f190d93663d0

1 in → 1 out12.3400 XPM110 B

ARjfZHEf…4npnTQw4

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.

2.551 × 10¹⁰⁸(109-digit number)

25511507187249211143…35583172614601053941

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

2.551 × 10¹⁰⁸(109-digit number)

25511507187249211143…35583172614601053941

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

5.102 × 10¹⁰⁸(109-digit number)

51023014374498422287…71166345229202107881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

1.020 × 10¹⁰⁹(110-digit number)

10204602874899684457…42332690458404215761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

2.040 × 10¹⁰⁹(110-digit number)

20409205749799368915…84665380916808431521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

4.081 × 10¹⁰⁹(110-digit number)

40818411499598737830…69330761833616863041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

8.163 × 10¹⁰⁹(110-digit number)

81636822999197475660…38661523667233726081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

1.632 × 10¹¹⁰(111-digit number)

16327364599839495132…77323047334467452161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

3.265 × 10¹¹⁰(111-digit number)

32654729199678990264…54646094668934904321

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

6.530 × 10¹¹⁰(111-digit number)

65309458399357980528…09292189337869808641

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