Block #300,488

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 12/8/2013, 3:09:27 PM · Difficulty 9.9923 · 6,494,892 confirmations

2CC

Cunningham Chain of the Second Kind

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

Block Header

Block Hash

8de02c3b0bb7142a9cedfa123652d36570f08096951fd5125590989ec2af71e7

View on Chainz ↗

Height

#300,488

Difficulty

9.992306

Transactions

Size

1.01 KB

Version

Bits

09fe07c2

Nonce

224,720

Timestamp

12/8/2013, 3:09:27 PM

Confirmations

6,494,892

Mined by

⛏️ aROAHZUHC8gzgPMTvVe1nqY6FNTrht3rBwmSA

Merkle Root

df964d79b06926ac10403ae97bb48c56406d75ef371aed5049f0fd0e8ce4689c

Transactions (1)

Coinbasedf964d79b06926…f0fd0e8ce4689c

1 in → 26 out10.0000 XPM947 B

AHZUHC8g…t3rBwmSA AZddc8bW…GLLasahx Ad9pSzHt…cpJ3y2zz AJjsX4t4…gtmJp9SX AUCeosP7…mw2ADT2w

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.

1.004 × 10⁹⁰(91-digit number)

10041814972304571234…63394630842622249921

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

1.004 × 10⁹⁰(91-digit number)

10041814972304571234…63394630842622249921

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^1 × origin + 1

2.008 × 10⁹⁰(91-digit number)

20083629944609142468…26789261685244499841

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^2 × origin + 1

4.016 × 10⁹⁰(91-digit number)

40167259889218284936…53578523370488999681

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^3 × origin + 1

8.033 × 10⁹⁰(91-digit number)

80334519778436569872…07157046740977999361

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^4 × origin + 1

1.606 × 10⁹¹(92-digit number)

16066903955687313974…14314093481955998721

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^5 × origin + 1

3.213 × 10⁹¹(92-digit number)

32133807911374627948…28628186963911997441

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^6 × origin + 1

6.426 × 10⁹¹(92-digit number)

64267615822749255897…57256373927823994881

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^7 × origin + 1

1.285 × 10⁹²(93-digit number)

12853523164549851179…14512747855647989761

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^8 × origin + 1

2.570 × 10⁹²(93-digit number)

25707046329099702359…29025495711295979521

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^9 × origin + 1

5.141 × 10⁹²(93-digit number)

51414092658199404718…58050991422591959041

Verify on FactorDB ↗Wolfram Alpha ↗

×2−1 →

2^10 × origin + 1

1.028 × 10⁹³(94-digit number)

10282818531639880943…16101982845183918081

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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