Block #273,507

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/25/2013, 8:21:51 PM · Difficulty 9.9550 · 6,516,370 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

a64a58ad988c1816fbe717e999f24eb7e78f785f54f29a99ee680f9134dc1e05

View on Chainz ↗

Height

#273,507

Difficulty

9.954992

Transactions

Size

2.44 KB

Version

Bits

09f47a59

Nonce

18,079

Timestamp

11/25/2013, 8:21:51 PM

Confirmations

6,516,370

Merkle Root

d488400ec1513dc8e4ccf8214c5872037722c88eb0a606da0cfb83ca9b08afb9

Transactions (4)

Coinbase152d2e1cf59bf6…9573804d3ffd1a

1 in → 1 out10.1200 XPM109 B

AKg576Sp…EnYaSDQx

0be530ce228797…6560ce34e1628b

2 in → 1 out124.9900 XPM339 B

ARVVKf6Q…6x1aCLJJ

cc049935f6e4f0…37c49a2d98acf9

11 in → 1 out195.3800 XPM1.26 KB

AWECTqwm…HsuLGUv5

383d236b7e4589…498950224ccef0

4 in → 2 out3.5310 XPM668 B

AaSPQSre…sBC9fTQR AMCmd7tx…tAaWXb1Y

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.

8.143 × 10⁹⁴(95-digit number)

81430048718382863304…83882900409309134721

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

8.143 × 10⁹⁴(95-digit number)

81430048718382863304…83882900409309134721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

1.628 × 10⁹⁵(96-digit number)

16286009743676572660…67765800818618269441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

3.257 × 10⁹⁵(96-digit number)

32572019487353145321…35531601637236538881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

6.514 × 10⁹⁵(96-digit number)

65144038974706290643…71063203274473077761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.302 × 10⁹⁶(97-digit number)

13028807794941258128…42126406548946155521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

2.605 × 10⁹⁶(97-digit number)

26057615589882516257…84252813097892311041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

5.211 × 10⁹⁶(97-digit number)

52115231179765032515…68505626195784622081

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.042 × 10⁹⁷(98-digit number)

10423046235953006503…37011252391569244161

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.084 × 10⁹⁷(98-digit number)

20846092471906013006…74022504783138488321

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