Block #504,932

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/22/2014, 2:52:47 AM · Difficulty 10.8099 · 6,312,727 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
651371c3e3258804c7750101c13296223061709f381fc9d2fb1a118787546c45

Height

#504,932

Difficulty

10.809882

Transactions

3

Size

661 B

Version

2

Bits

0acf5470

Nonce

38,630

Timestamp

4/22/2014, 2:52:47 AM

Confirmations

6,312,727

Merkle Root

3cc35ba4e33df94187d31f8c4949bf3678a9ac56189d980142243a95f445a702
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.

1.231 × 10¹⁰¹(102-digit number)
12313399258364566843…33525040724915077121
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
1.231 × 10¹⁰¹(102-digit number)
12313399258364566843…33525040724915077121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.462 × 10¹⁰¹(102-digit number)
24626798516729133687…67050081449830154241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.925 × 10¹⁰¹(102-digit number)
49253597033458267375…34100162899660308481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.850 × 10¹⁰¹(102-digit number)
98507194066916534750…68200325799320616961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.970 × 10¹⁰²(103-digit number)
19701438813383306950…36400651598641233921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.940 × 10¹⁰²(103-digit number)
39402877626766613900…72801303197282467841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.880 × 10¹⁰²(103-digit number)
78805755253533227800…45602606394564935681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.576 × 10¹⁰³(104-digit number)
15761151050706645560…91205212789129871361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.152 × 10¹⁰³(104-digit number)
31522302101413291120…82410425578259742721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.304 × 10¹⁰³(104-digit number)
63044604202826582240…64820851156519485441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.260 × 10¹⁰⁴(105-digit number)
12608920840565316448…29641702313038970881
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:57,785,326 XPM·at block #6,817,658 · updates every 60s
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