Block #1,408,311

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/11/2016, 6:05:12 AM · Difficulty 10.8041 · 5,432,811 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ab63aee401c8f7c6222e0b85f3196a57e2c4b13afd941c3904ccf6763e3cbd20

Height

#1,408,311

Difficulty

10.804075

Transactions

2

Size

969 B

Version

2

Bits

0acdd7d6

Nonce

10,634,526

Timestamp

1/11/2016, 6:05:12 AM

Confirmations

5,432,811

Merkle Root

fc3ff0b28e687c675729509ec26fbbfc988a1b9532057601b9467d1813b11aad
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.

2.213 × 10⁹³(94-digit number)
22132628103185446883…56404156440329789641
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
2.213 × 10⁹³(94-digit number)
22132628103185446883…56404156440329789641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.426 × 10⁹³(94-digit number)
44265256206370893767…12808312880659579281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
8.853 × 10⁹³(94-digit number)
88530512412741787534…25616625761319158561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.770 × 10⁹⁴(95-digit number)
17706102482548357506…51233251522638317121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.541 × 10⁹⁴(95-digit number)
35412204965096715013…02466503045276634241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.082 × 10⁹⁴(95-digit number)
70824409930193430027…04933006090553268481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.416 × 10⁹⁵(96-digit number)
14164881986038686005…09866012181106536961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.832 × 10⁹⁵(96-digit number)
28329763972077372011…19732024362213073921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.665 × 10⁹⁵(96-digit number)
56659527944154744022…39464048724426147841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.133 × 10⁹⁶(97-digit number)
11331905588830948804…78928097448852295681
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:57,973,345 XPM·at block #6,841,121 · updates every 60s
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