Block #1,268,400

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/5/2015, 6:05:03 PM · Difficulty 10.8169 · 5,548,606 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
aac988be06faf9d04e2afeb1c2d19eb863bddbeed8d6dffab72d454419d2e9c9

Height

#1,268,400

Difficulty

10.816911

Transactions

4

Size

1.58 KB

Version

2

Bits

0ad1211b

Nonce

625,820,976

Timestamp

10/5/2015, 6:05:03 PM

Confirmations

5,548,606

Merkle Root

0169d4000f93477b68698965d8da9707279030894c178a620d30214443c1fcd0
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.

1.864 × 10⁹⁴(95-digit number)
18646566373210825178…71336108616173357441
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
1.864 × 10⁹⁴(95-digit number)
18646566373210825178…71336108616173357441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.729 × 10⁹⁴(95-digit number)
37293132746421650357…42672217232346714881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.458 × 10⁹⁴(95-digit number)
74586265492843300715…85344434464693429761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.491 × 10⁹⁵(96-digit number)
14917253098568660143…70688868929386859521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.983 × 10⁹⁵(96-digit number)
29834506197137320286…41377737858773719041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.966 × 10⁹⁵(96-digit number)
59669012394274640572…82755475717547438081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.193 × 10⁹⁶(97-digit number)
11933802478854928114…65510951435094876161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.386 × 10⁹⁶(97-digit number)
23867604957709856229…31021902870189752321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.773 × 10⁹⁶(97-digit number)
47735209915419712458…62043805740379504641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.547 × 10⁹⁶(97-digit number)
95470419830839424916…24087611480759009281
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:57,780,081 XPM·at block #6,817,005 · updates every 60s
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