Block #600,180

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 6/24/2014, 12:08:34 PM · Difficulty 10.9187 · 6,217,150 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f6f3e094767e9478607cf56ba1810cfbdb6272f9507d5beb50729c2359814666

Height

#600,180

Difficulty

10.918655

Transactions

4

Size

4.33 KB

Version

2

Bits

0aeb2cfd

Nonce

343,451,379

Timestamp

6/24/2014, 12:08:34 PM

Confirmations

6,217,150

Merkle Root

290c64f136bac3cb0d53c14ca7bd6b21b3b29c97fd02e8b0efc1ed2b9244cc20
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.

1.148 × 10⁹⁶(97-digit number)
11482430210136109241…67747829195215177901
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
1.148 × 10⁹⁶(97-digit number)
11482430210136109241…67747829195215177901
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.296 × 10⁹⁶(97-digit number)
22964860420272218483…35495658390430355801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.592 × 10⁹⁶(97-digit number)
45929720840544436967…70991316780860711601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.185 × 10⁹⁶(97-digit number)
91859441681088873934…41982633561721423201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.837 × 10⁹⁷(98-digit number)
18371888336217774786…83965267123442846401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.674 × 10⁹⁷(98-digit number)
36743776672435549573…67930534246885692801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.348 × 10⁹⁷(98-digit number)
73487553344871099147…35861068493771385601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.469 × 10⁹⁸(99-digit number)
14697510668974219829…71722136987542771201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.939 × 10⁹⁸(99-digit number)
29395021337948439659…43444273975085542401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.879 × 10⁹⁸(99-digit number)
58790042675896879318…86888547950171084801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.175 × 10⁹⁹(100-digit number)
11758008535179375863…73777095900342169601
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:57,782,686 XPM·at block #6,817,329 · updates every 60s
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