Block #483,733

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 5:17:07 AM · Difficulty 10.5688 · 6,358,672 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
483025c81df6d342af73a6e36d3ae7bad1aeabd497e73da6243f977c1770fb6a

Height

#483,733

Difficulty

10.568760

Transactions

1

Size

764 B

Version

2

Bits

0a919a45

Nonce

348,132

Timestamp

4/10/2014, 5:17:07 AM

Confirmations

6,358,672

Merkle Root

4e807d635f26a80dae0d9542d7d28f1ff7b55abaee3acfe0ce3db13e0fab2abd
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.

2.678 × 10⁹²(93-digit number)
26784190439636167655…84183267537421600641
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
2.678 × 10⁹²(93-digit number)
26784190439636167655…84183267537421600641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.356 × 10⁹²(93-digit number)
53568380879272335310…68366535074843201281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.071 × 10⁹³(94-digit number)
10713676175854467062…36733070149686402561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.142 × 10⁹³(94-digit number)
21427352351708934124…73466140299372805121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.285 × 10⁹³(94-digit number)
42854704703417868248…46932280598745610241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.570 × 10⁹³(94-digit number)
85709409406835736497…93864561197491220481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.714 × 10⁹⁴(95-digit number)
17141881881367147299…87729122394982440961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.428 × 10⁹⁴(95-digit number)
34283763762734294598…75458244789964881921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.856 × 10⁹⁴(95-digit number)
68567527525468589197…50916489579929763841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.371 × 10⁹⁵(96-digit number)
13713505505093717839…01832979159859527681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
2.742 × 10⁹⁵(96-digit number)
27427011010187435679…03665958319719055361
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:57,983,652 XPM·at block #6,842,404 · updates every 60s
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