Block #1,392,830

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 12/31/2015, 9:49:40 AM · Difficulty 10.8088 · 5,424,178 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4cff2c3490f2d3e1d6f1ecd104a919e0856a96d02c7e5d54fd0ba98017f35352

Height

#1,392,830

Difficulty

10.808765

Transactions

4

Size

2.06 KB

Version

2

Bits

0acf0b37

Nonce

1,886,387,406

Timestamp

12/31/2015, 9:49:40 AM

Confirmations

5,424,178

Merkle Root

f9c5e8020b03286ee956b5f4d68b0f1ed47a67a3fea701b362c13b34aabac00c
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.

2.041 × 10⁹²(93-digit number)
20410594690480042399…75344067249474008141
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
2.041 × 10⁹²(93-digit number)
20410594690480042399…75344067249474008141
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.082 × 10⁹²(93-digit number)
40821189380960084798…50688134498948016281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.164 × 10⁹²(93-digit number)
81642378761920169597…01376268997896032561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.632 × 10⁹³(94-digit number)
16328475752384033919…02752537995792065121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.265 × 10⁹³(94-digit number)
32656951504768067839…05505075991584130241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
6.531 × 10⁹³(94-digit number)
65313903009536135678…11010151983168260481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.306 × 10⁹⁴(95-digit number)
13062780601907227135…22020303966336520961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.612 × 10⁹⁴(95-digit number)
26125561203814454271…44040607932673041921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.225 × 10⁹⁴(95-digit number)
52251122407628908542…88081215865346083841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.045 × 10⁹⁵(96-digit number)
10450224481525781708…76162431730692167681
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:57,780,098 XPM·at block #6,817,007 · updates every 60s
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