Block #482,160

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/9/2014, 8:18:24 AM · Difficulty 10.5404 · 6,313,219 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
9b3a16e9d487df3491d26a472cea35cee7b3930650b0cd701506910d7da52060

Height

#482,160

Difficulty

10.540439

Transactions

3

Size

2.07 KB

Version

2

Bits

0a8a5a35

Nonce

66,896

Timestamp

4/9/2014, 8:18:24 AM

Confirmations

6,313,219

Merkle Root

01eda662fa69c284388aa2d054e520ff29678a6bf574c7e8c23d1da2270de4fa
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.

1.861 × 10¹⁰²(103-digit number)
18615857069696360989…51884184787439385599
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
1.861 × 10¹⁰²(103-digit number)
18615857069696360989…51884184787439385599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.723 × 10¹⁰²(103-digit number)
37231714139392721978…03768369574878771199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.446 × 10¹⁰²(103-digit number)
74463428278785443957…07536739149757542399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.489 × 10¹⁰³(104-digit number)
14892685655757088791…15073478299515084799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.978 × 10¹⁰³(104-digit number)
29785371311514177583…30146956599030169599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.957 × 10¹⁰³(104-digit number)
59570742623028355166…60293913198060339199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.191 × 10¹⁰⁴(105-digit number)
11914148524605671033…20587826396120678399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.382 × 10¹⁰⁴(105-digit number)
23828297049211342066…41175652792241356799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
4.765 × 10¹⁰⁴(105-digit number)
47656594098422684133…82351305584482713599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
9.531 × 10¹⁰⁴(105-digit number)
95313188196845368266…64702611168965427199
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:57,607,090 XPM·at block #6,795,378 · updates every 60s
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