Block #611,855

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 7/2/2014, 9:00:38 AM · Difficulty 10.9244 · 6,194,325 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
70debd1700639ecf1dd8c2080b2ba8b0c2051bec6e79d6dc70f70347f95bb521

Height

#611,855

Difficulty

10.924407

Transactions

4

Size

7.66 KB

Version

2

Bits

0aeca5ea

Nonce

37,827,378

Timestamp

7/2/2014, 9:00:38 AM

Confirmations

6,194,325

Merkle Root

2c2c44cafa697c50a1b821db2a67e9cdd4e1a8fb361d5a1cea00f5244d0afe7b
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.

3.983 × 10⁹⁷(98-digit number)
39833212142956137295…77612797461236992001
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.

1
origin + 1
3.983 × 10⁹⁷(98-digit number)
39833212142956137295…77612797461236992001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.966 × 10⁹⁷(98-digit number)
79666424285912274591…55225594922473984001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.593 × 10⁹⁸(99-digit number)
15933284857182454918…10451189844947968001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.186 × 10⁹⁸(99-digit number)
31866569714364909836…20902379689895936001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.373 × 10⁹⁸(99-digit number)
63733139428729819673…41804759379791872001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.274 × 10⁹⁹(100-digit number)
12746627885745963934…83609518759583744001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.549 × 10⁹⁹(100-digit number)
25493255771491927869…67219037519167488001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.098 × 10⁹⁹(100-digit number)
50986511542983855738…34438075038334976001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.019 × 10¹⁰⁰(101-digit number)
10197302308596771147…68876150076669952001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.039 × 10¹⁰⁰(101-digit number)
20394604617193542295…37752300153339904001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.078 × 10¹⁰⁰(101-digit number)
40789209234387084591…75504600306679808001
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, …
Circulating Supply:57,693,524 XPM·at block #6,806,179 · updates every 60s
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