Block #484,401

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 1:06:34 PM · Difficulty 10.5853 · 6,324,213 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e85e0d4ff661bb4042c9c6dc50c4ed50b87d35ae0984f66c1f9a04576637a5a3

Height

#484,401

Difficulty

10.585255

Transactions

1

Size

800 B

Version

2

Bits

0a95d34c

Nonce

5,304

Timestamp

4/10/2014, 1:06:34 PM

Confirmations

6,324,213

Merkle Root

ec3984a7dbc19736cea499b9ddb89bb0689c09671c81690dd9505b316b4b6d52
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.

8.537 × 10⁹⁷(98-digit number)
85376639742333886173…49948849988503234521
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
8.537 × 10⁹⁷(98-digit number)
85376639742333886173…49948849988503234521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.707 × 10⁹⁸(99-digit number)
17075327948466777234…99897699977006469041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.415 × 10⁹⁸(99-digit number)
34150655896933554469…99795399954012938081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.830 × 10⁹⁸(99-digit number)
68301311793867108939…99590799908025876161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.366 × 10⁹⁹(100-digit number)
13660262358773421787…99181599816051752321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.732 × 10⁹⁹(100-digit number)
27320524717546843575…98363199632103504641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.464 × 10⁹⁹(100-digit number)
54641049435093687151…96726399264207009281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.092 × 10¹⁰⁰(101-digit number)
10928209887018737430…93452798528414018561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.185 × 10¹⁰⁰(101-digit number)
21856419774037474860…86905597056828037121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.371 × 10¹⁰⁰(101-digit number)
43712839548074949720…73811194113656074241
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:57,712,962 XPM·at block #6,808,613 · updates every 60s
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