Block #227,955

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/26/2013, 5:14:37 AM · Difficulty 9.9372 · 6,574,614 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c62dbb8870b7a85ee0f865dad0886d167085e71761a5d57867343da12bb24898

Height

#227,955

Difficulty

9.937203

Transactions

6

Size

2.71 KB

Version

2

Bits

09efec8c

Nonce

19,742

Timestamp

10/26/2013, 5:14:37 AM

Confirmations

6,574,614

Merkle Root

797830122cb6d2c1dd7b8f1d9dcc8a1c0a7f3a14a0a8f5ceed8b73ac7b2bc46f
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.

1.679 × 10⁹²(93-digit number)
16794024528330660676…54336084302108649081
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
1.679 × 10⁹²(93-digit number)
16794024528330660676…54336084302108649081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.358 × 10⁹²(93-digit number)
33588049056661321353…08672168604217298161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
6.717 × 10⁹²(93-digit number)
67176098113322642707…17344337208434596321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.343 × 10⁹³(94-digit number)
13435219622664528541…34688674416869192641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.687 × 10⁹³(94-digit number)
26870439245329057082…69377348833738385281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.374 × 10⁹³(94-digit number)
53740878490658114165…38754697667476770561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.074 × 10⁹⁴(95-digit number)
10748175698131622833…77509395334953541121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.149 × 10⁹⁴(95-digit number)
21496351396263245666…55018790669907082241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.299 × 10⁹⁴(95-digit number)
42992702792526491332…10037581339814164481
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, …
Circulating Supply:57,664,567 XPM·at block #6,802,568 · updates every 60s
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