Block #487,006

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 9:48:39 PM · Difficulty 10.6355 · 6,322,495 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
db1b1710bc3526e1b79fcc44724fd37471b8d538051ba3ffd01784f1082e2717

Height

#487,006

Difficulty

10.635532

Transactions

1

Size

865 B

Version

2

Bits

0aa2b23a

Nonce

515,866

Timestamp

4/11/2014, 9:48:39 PM

Confirmations

6,322,495

Merkle Root

5163b8aeb1b03afe0fbe24c1794b56447ab6ed9fad6a08fe52d4234891b472b0
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.

2.065 × 10⁹²(93-digit number)
20650592869252382433…28536581043284968961
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
2.065 × 10⁹²(93-digit number)
20650592869252382433…28536581043284968961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.130 × 10⁹²(93-digit number)
41301185738504764867…57073162086569937921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.260 × 10⁹²(93-digit number)
82602371477009529734…14146324173139875841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.652 × 10⁹³(94-digit number)
16520474295401905946…28292648346279751681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.304 × 10⁹³(94-digit number)
33040948590803811893…56585296692559503361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.608 × 10⁹³(94-digit number)
66081897181607623787…13170593385119006721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.321 × 10⁹⁴(95-digit number)
13216379436321524757…26341186770238013441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.643 × 10⁹⁴(95-digit number)
26432758872643049515…52682373540476026881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.286 × 10⁹⁴(95-digit number)
52865517745286099030…05364747080952053761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.057 × 10⁹⁵(96-digit number)
10573103549057219806…10729494161904107521
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,720,081 XPM·at block #6,809,500 · updates every 60s
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