Block #480,519

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/8/2014, 8:50:53 AM · Difficulty 10.5177 · 6,335,747 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a2492c2a1ad9b2b70fdac057eae53eb1b6a04f41a4f75999245c41228d9fb6a2

Height

#480,519

Difficulty

10.517709

Transactions

1

Size

1003 B

Version

2

Bits

0a848896

Nonce

154,808

Timestamp

4/8/2014, 8:50:53 AM

Confirmations

6,335,747

Merkle Root

7f6c052409cec47f09f29f824c43d50a28f3a61a43695223df80915f4ee30105
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.

5.615 × 10⁹⁴(95-digit number)
56156772704252431988…67490302981226808961
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
5.615 × 10⁹⁴(95-digit number)
56156772704252431988…67490302981226808961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.123 × 10⁹⁵(96-digit number)
11231354540850486397…34980605962453617921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.246 × 10⁹⁵(96-digit number)
22462709081700972795…69961211924907235841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.492 × 10⁹⁵(96-digit number)
44925418163401945590…39922423849814471681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.985 × 10⁹⁵(96-digit number)
89850836326803891181…79844847699628943361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.797 × 10⁹⁶(97-digit number)
17970167265360778236…59689695399257886721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.594 × 10⁹⁶(97-digit number)
35940334530721556472…19379390798515773441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.188 × 10⁹⁶(97-digit number)
71880669061443112945…38758781597031546881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.437 × 10⁹⁷(98-digit number)
14376133812288622589…77517563194063093761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.875 × 10⁹⁷(98-digit number)
28752267624577245178…55035126388126187521
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:57,774,241 XPM·at block #6,816,265 · updates every 60s
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