Block #1,494,354

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/12/2016, 11:05:33 PM · Difficulty 10.6616 · 5,350,345 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
b2ced5dbd8dbc565381b7a0269dfb0e5686ae102dc0f4c83f1502b483592e1d9

Height

#1,494,354

Difficulty

10.661628

Transactions

2

Size

1.08 KB

Version

2

Bits

0aa9606e

Nonce

72,899,929

Timestamp

3/12/2016, 11:05:33 PM

Confirmations

5,350,345

Merkle Root

37ef05f873bdf9dd1c6f02775a2c9a3ebf2a04dba581aedba5fa5190c811ea3d
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.

9.969 × 10⁹¹(92-digit number)
99696938166717112605…68673282290087666361
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
9.969 × 10⁹¹(92-digit number)
99696938166717112605…68673282290087666361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.993 × 10⁹²(93-digit number)
19939387633343422521…37346564580175332721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.987 × 10⁹²(93-digit number)
39878775266686845042…74693129160350665441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
7.975 × 10⁹²(93-digit number)
79757550533373690084…49386258320701330881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.595 × 10⁹³(94-digit number)
15951510106674738016…98772516641402661761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.190 × 10⁹³(94-digit number)
31903020213349476033…97545033282805323521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.380 × 10⁹³(94-digit number)
63806040426698952067…95090066565610647041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.276 × 10⁹⁴(95-digit number)
12761208085339790413…90180133131221294081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.552 × 10⁹⁴(95-digit number)
25522416170679580826…80360266262442588161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.104 × 10⁹⁴(95-digit number)
51044832341359161653…60720532524885176321
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:58,002,002 XPM·at block #6,844,698 · updates every 60s
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