Block #384,948

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 2/1/2014, 11:18:04 AM · Difficulty 10.4028 · 6,414,492 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
33ddff008b60e1c7b11506b60be8b1674085b53220a90ab7f642ac5181e6dacf

Height

#384,948

Difficulty

10.402772

Transactions

3

Size

774 B

Version

2

Bits

0a671c13

Nonce

58,374

Timestamp

2/1/2014, 11:18:04 AM

Confirmations

6,414,492

Merkle Root

889aff85942fdca3c1d5bb81a78c3533facf96eac4a2fcfd065df5d5a229526f
Transactions (3)
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.

2.402 × 10⁹⁴(95-digit number)
24029730700659907146…67108466355899184001
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
2.402 × 10⁹⁴(95-digit number)
24029730700659907146…67108466355899184001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.805 × 10⁹⁴(95-digit number)
48059461401319814293…34216932711798368001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.611 × 10⁹⁴(95-digit number)
96118922802639628586…68433865423596736001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.922 × 10⁹⁵(96-digit number)
19223784560527925717…36867730847193472001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.844 × 10⁹⁵(96-digit number)
38447569121055851434…73735461694386944001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.689 × 10⁹⁵(96-digit number)
76895138242111702869…47470923388773888001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.537 × 10⁹⁶(97-digit number)
15379027648422340573…94941846777547776001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.075 × 10⁹⁶(97-digit number)
30758055296844681147…89883693555095552001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.151 × 10⁹⁶(97-digit number)
61516110593689362295…79767387110191104001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.230 × 10⁹⁷(98-digit number)
12303222118737872459…59534774220382208001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.460 × 10⁹⁷(98-digit number)
24606444237475744918…19069548440764416001
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:57,639,571 XPM·at block #6,799,439 · updates every 60s
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