Block #892,567

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/12/2015, 4:48:26 PM · Difficulty 10.9521 · 5,913,777 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4784d90a7a9dc4f28e73c2f0e2b5784a333c26578d27cd2161e40fc17e28ff56

Height

#892,567

Difficulty

10.952092

Transactions

5

Size

1.23 KB

Version

2

Bits

0af3bc50

Nonce

2,332,649,099

Timestamp

1/12/2015, 4:48:26 PM

Confirmations

5,913,777

Merkle Root

3b937118f764c67d24403c8b9532dc22bfc4946a0d21441498fac69e25c4de1b
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.

1.245 × 10⁹⁶(97-digit number)
12456525162312935451…57465458180929491841
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
1.245 × 10⁹⁶(97-digit number)
12456525162312935451…57465458180929491841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.491 × 10⁹⁶(97-digit number)
24913050324625870903…14930916361858983681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.982 × 10⁹⁶(97-digit number)
49826100649251741807…29861832723717967361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.965 × 10⁹⁶(97-digit number)
99652201298503483614…59723665447435934721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.993 × 10⁹⁷(98-digit number)
19930440259700696722…19447330894871869441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.986 × 10⁹⁷(98-digit number)
39860880519401393445…38894661789743738881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.972 × 10⁹⁷(98-digit number)
79721761038802786891…77789323579487477761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.594 × 10⁹⁸(99-digit number)
15944352207760557378…55578647158974955521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.188 × 10⁹⁸(99-digit number)
31888704415521114756…11157294317949911041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.377 × 10⁹⁸(99-digit number)
63777408831042229513…22314588635899822081
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:57,694,837 XPM·at block #6,806,343 · updates every 60s
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