Block #479,547

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/7/2014, 6:10:28 PM · Difficulty 10.5085 · 6,334,473 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
d69df570499828d54062061f40bed0ef70f9cbe6a80f09b90e2b2ce292865baa

Height

#479,547

Difficulty

10.508517

Transactions

1

Size

832 B

Version

2

Bits

0a822e2c

Nonce

326,010

Timestamp

4/7/2014, 6:10:28 PM

Confirmations

6,334,473

Merkle Root

a06419dfbb4b52193924a6c81ab5d031efdd6a7fc3f619d9f407e19924db91d0
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.

5.294 × 10⁹²(93-digit number)
52941775672210053193…30535468915051603441
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
5.294 × 10⁹²(93-digit number)
52941775672210053193…30535468915051603441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.058 × 10⁹³(94-digit number)
10588355134442010638…61070937830103206881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.117 × 10⁹³(94-digit number)
21176710268884021277…22141875660206413761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.235 × 10⁹³(94-digit number)
42353420537768042554…44283751320412827521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.470 × 10⁹³(94-digit number)
84706841075536085109…88567502640825655041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.694 × 10⁹⁴(95-digit number)
16941368215107217021…77135005281651310081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.388 × 10⁹⁴(95-digit number)
33882736430214434043…54270010563302620161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.776 × 10⁹⁴(95-digit number)
67765472860428868087…08540021126605240321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.355 × 10⁹⁵(96-digit number)
13553094572085773617…17080042253210480641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.710 × 10⁹⁵(96-digit number)
27106189144171547234…34160084506420961281
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:57,756,244 XPM·at block #6,814,019 · updates every 60s
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