Block #930,842

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/10/2015, 8:11:34 PM · Difficulty 10.9022 · 5,866,016 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2ff9bfce6b54702b3ee0a4eda2d2337f72810d084dd0f3066d217c7090116c5a

Height

#930,842

Difficulty

10.902165

Transactions

3

Size

7.00 KB

Version

2

Bits

0ae6f446

Nonce

618,034,870

Timestamp

2/10/2015, 8:11:34 PM

Confirmations

5,866,016

Merkle Root

992a9f67dccb98cbc3cc5e9681978a84c98356d3c03d8a9128ae3af6581500e9
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.

8.778 × 10⁹⁵(96-digit number)
87782135217934070157…61856034675030333331
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
8.778 × 10⁹⁵(96-digit number)
87782135217934070157…61856034675030333331
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.755 × 10⁹⁶(97-digit number)
17556427043586814031…23712069350060666661
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.511 × 10⁹⁶(97-digit number)
35112854087173628063…47424138700121333321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.022 × 10⁹⁶(97-digit number)
70225708174347256126…94848277400242666641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.404 × 10⁹⁷(98-digit number)
14045141634869451225…89696554800485333281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.809 × 10⁹⁷(98-digit number)
28090283269738902450…79393109600970666561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.618 × 10⁹⁷(98-digit number)
56180566539477804900…58786219201941333121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.123 × 10⁹⁸(99-digit number)
11236113307895560980…17572438403882666241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.247 × 10⁹⁸(99-digit number)
22472226615791121960…35144876807765332481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.494 × 10⁹⁸(99-digit number)
44944453231582243920…70289753615530664961
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:57,618,877 XPM·at block #6,796,857 · updates every 60s
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