Block #485,422

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/11/2014, 1:20:07 AM · Difficulty 10.6085 · 6,329,718 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
e84dbac3077de0a58cfd9c6d4cf1356d2cdecc0f835505be39484ae4870ae400

Height

#485,422

Difficulty

10.608468

Transactions

4

Size

878 B

Version

2

Bits

0a9bc487

Nonce

1,029,758,815

Timestamp

4/11/2014, 1:20:07 AM

Confirmations

6,329,718

Merkle Root

e0d7e6e85d698056966b6335935c37b0200433031fd2b211335a6a8c0969bab7
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.

1.052 × 10⁹⁴(95-digit number)
10522967773932811974…96374866569916779401
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
1.052 × 10⁹⁴(95-digit number)
10522967773932811974…96374866569916779401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.104 × 10⁹⁴(95-digit number)
21045935547865623949…92749733139833558801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.209 × 10⁹⁴(95-digit number)
42091871095731247898…85499466279667117601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.418 × 10⁹⁴(95-digit number)
84183742191462495796…70998932559334235201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.683 × 10⁹⁵(96-digit number)
16836748438292499159…41997865118668470401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.367 × 10⁹⁵(96-digit number)
33673496876584998318…83995730237336940801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.734 × 10⁹⁵(96-digit number)
67346993753169996637…67991460474673881601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.346 × 10⁹⁶(97-digit number)
13469398750633999327…35982920949347763201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.693 × 10⁹⁶(97-digit number)
26938797501267998654…71965841898695526401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.387 × 10⁹⁶(97-digit number)
53877595002535997309…43931683797391052801
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:57,765,214 XPM·at block #6,815,139 · updates every 60s
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