Block #1,002,032

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/4/2015, 10:16:53 AM · Difficulty 10.7648 · 5,806,593 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
458d2cc0f905744ba057978e47afe3c144792a8b1ac186119c0fd862d0f1ef4d

Height

#1,002,032

Difficulty

10.764846

Transactions

4

Size

1.01 KB

Version

2

Bits

0ac3cceb

Nonce

74,081,033

Timestamp

4/4/2015, 10:16:53 AM

Confirmations

5,806,593

Merkle Root

603b4e710bfa1b7d673f9c8fdf2d58d32f2d683da516a448a833bcad69b44dca
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.

1.059 × 10⁹⁶(97-digit number)
10598520973635124431…98495777289331820001
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
1.059 × 10⁹⁶(97-digit number)
10598520973635124431…98495777289331820001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.119 × 10⁹⁶(97-digit number)
21197041947270248863…96991554578663640001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.239 × 10⁹⁶(97-digit number)
42394083894540497727…93983109157327280001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.478 × 10⁹⁶(97-digit number)
84788167789080995454…87966218314654560001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.695 × 10⁹⁷(98-digit number)
16957633557816199090…75932436629309120001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.391 × 10⁹⁷(98-digit number)
33915267115632398181…51864873258618240001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.783 × 10⁹⁷(98-digit number)
67830534231264796363…03729746517236480001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.356 × 10⁹⁸(99-digit number)
13566106846252959272…07459493034472960001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.713 × 10⁹⁸(99-digit number)
27132213692505918545…14918986068945920001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.426 × 10⁹⁸(99-digit number)
54264427385011837091…29837972137891840001
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:57,713,051 XPM·at block #6,808,624 · updates every 60s
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