Block #486,183

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/11/2014, 11:26:02 AM · Difficulty 10.6205 · 6,323,514 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
106152e25357a3beba5de3aad42ea5330246ecf2cc63b619e288d1c79d8fba26

Height

#486,183

Difficulty

10.620540

Transactions

2

Size

2.42 KB

Version

2

Bits

0a9edbbe

Nonce

152,786,048

Timestamp

4/11/2014, 11:26:02 AM

Confirmations

6,323,514

Merkle Root

682b70b5a0882499d3e9cba24bace2d40324cb53bfca10999fee8aaafa247ac4
Transactions (2)
1 in → 1 out8.8800 XPM116 B
15 in → 1 out45.9526 XPM2.21 KB
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.

4.550 × 10⁹⁹(100-digit number)
45503802702993820649…87342342153140180479
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
4.550 × 10⁹⁹(100-digit number)
45503802702993820649…87342342153140180479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.100 × 10⁹⁹(100-digit number)
91007605405987641298…74684684306280360959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.820 × 10¹⁰⁰(101-digit number)
18201521081197528259…49369368612560721919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.640 × 10¹⁰⁰(101-digit number)
36403042162395056519…98738737225121443839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.280 × 10¹⁰⁰(101-digit number)
72806084324790113038…97477474450242887679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.456 × 10¹⁰¹(102-digit number)
14561216864958022607…94954948900485775359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.912 × 10¹⁰¹(102-digit number)
29122433729916045215…89909897800971550719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.824 × 10¹⁰¹(102-digit number)
58244867459832090430…79819795601943101439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.164 × 10¹⁰²(103-digit number)
11648973491966418086…59639591203886202879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.329 × 10¹⁰²(103-digit number)
23297946983932836172…19279182407772405759
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,721,653 XPM·at block #6,809,696 · updates every 60s
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