Block #487,323

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/12/2014, 2:18:21 AM · Difficulty 10.6389 · 6,309,196 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f926fcc228ff1978e6b0e4d5484f4866b910da20b0ac4cfc1232ab41d07ad3a0

Height

#487,323

Difficulty

10.638879

Transactions

4

Size

1.15 KB

Version

2

Bits

0aa38d90

Nonce

242,672,471

Timestamp

4/12/2014, 2:18:21 AM

Confirmations

6,309,196

Merkle Root

cd3a8f2ff8588cce40fe79425f091d716ea3a176e8e7edf8bafa9b43fd3e556c
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.

4.520 × 10⁹⁸(99-digit number)
45209871887945076113…72724704311842199679
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
4.520 × 10⁹⁸(99-digit number)
45209871887945076113…72724704311842199679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.041 × 10⁹⁸(99-digit number)
90419743775890152227…45449408623684399359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.808 × 10⁹⁹(100-digit number)
18083948755178030445…90898817247368798719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.616 × 10⁹⁹(100-digit number)
36167897510356060890…81797634494737597439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.233 × 10⁹⁹(100-digit number)
72335795020712121781…63595268989475194879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.446 × 10¹⁰⁰(101-digit number)
14467159004142424356…27190537978950389759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.893 × 10¹⁰⁰(101-digit number)
28934318008284848712…54381075957900779519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
5.786 × 10¹⁰⁰(101-digit number)
57868636016569697425…08762151915801559039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.157 × 10¹⁰¹(102-digit number)
11573727203313939485…17524303831603118079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.314 × 10¹⁰¹(102-digit number)
23147454406627878970…35048607663206236159
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:57,616,149 XPM·at block #6,796,518 · updates every 60s
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