Block #1,494,135

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/12/2016, 7:04:35 PM · Difficulty 10.6632 · 5,332,629 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
02e18d98ac2b39be7e5c3b6db092401a186b8ec008584bb6d14b9e0f11d0afb4

Height

#1,494,135

Difficulty

10.663170

Transactions

2

Size

1.15 KB

Version

2

Bits

0aa9c583

Nonce

717,296,837

Timestamp

3/12/2016, 7:04:35 PM

Confirmations

5,332,629

Merkle Root

ffed2e2e4a7ada68a4f0f742451d143ad59c3ed5638332e8a6bc5fe70e3a7de1
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.

3.392 × 10⁹³(94-digit number)
33929987249571406617…55827250250626490881
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
3.392 × 10⁹³(94-digit number)
33929987249571406617…55827250250626490881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.785 × 10⁹³(94-digit number)
67859974499142813234…11654500501252981761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.357 × 10⁹⁴(95-digit number)
13571994899828562646…23309001002505963521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.714 × 10⁹⁴(95-digit number)
27143989799657125293…46618002005011927041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.428 × 10⁹⁴(95-digit number)
54287979599314250587…93236004010023854081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.085 × 10⁹⁵(96-digit number)
10857595919862850117…86472008020047708161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.171 × 10⁹⁵(96-digit number)
21715191839725700234…72944016040095416321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.343 × 10⁹⁵(96-digit number)
43430383679451400469…45888032080190832641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.686 × 10⁹⁵(96-digit number)
86860767358902800939…91776064160381665281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.737 × 10⁹⁶(97-digit number)
17372153471780560187…83552128320763330561
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:57,858,272 XPM·at block #6,826,763 · updates every 60s
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