Block #485,287

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/10/2014, 11:36:45 PM · Difficulty 10.6060 · 6,325,712 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ed5bf93f0bbfa01c3b4a1d9dd797aeff1f809ae8871cadb6a472369d8a4c172d

Height

#485,287

Difficulty

10.606019

Transactions

3

Size

806 B

Version

2

Bits

0a9b2416

Nonce

133,448,650

Timestamp

4/10/2014, 11:36:45 PM

Confirmations

6,325,712

Merkle Root

87b3ad184489fd0c25c0633dbe1e85a6c07373eced1c0372be97632aeea0dd69
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.

1.050 × 10¹⁰⁰(101-digit number)
10508818767879717979…96138818974471393281
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
1.050 × 10¹⁰⁰(101-digit number)
10508818767879717979…96138818974471393281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.101 × 10¹⁰⁰(101-digit number)
21017637535759435959…92277637948942786561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.203 × 10¹⁰⁰(101-digit number)
42035275071518871919…84555275897885573121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.407 × 10¹⁰⁰(101-digit number)
84070550143037743839…69110551795771146241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.681 × 10¹⁰¹(102-digit number)
16814110028607548767…38221103591542292481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.362 × 10¹⁰¹(102-digit number)
33628220057215097535…76442207183084584961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.725 × 10¹⁰¹(102-digit number)
67256440114430195071…52884414366169169921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.345 × 10¹⁰²(103-digit number)
13451288022886039014…05768828732338339841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.690 × 10¹⁰²(103-digit number)
26902576045772078028…11537657464676679681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.380 × 10¹⁰²(103-digit number)
53805152091544156057…23075314929353359361
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:57,732,095 XPM·at block #6,810,998 · updates every 60s
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