Block #483,019

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/9/2014, 8:05:26 PM · Difficulty 10.5542 · 6,327,807 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
cd65195ab3e19dcdc96129f872a085130edb13d075a8a86253977574db633a47

Height

#483,019

Difficulty

10.554238

Transactions

2

Size

2.78 KB

Version

2

Bits

0a8de287

Nonce

201,328,615

Timestamp

4/9/2014, 8:05:26 PM

Confirmations

6,327,807

Merkle Root

56a6b46d278d3a3c9f64164dbf811fa208d6dcaf4bd56655dce3c528ed5b0008
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.

1.210 × 10⁹⁷(98-digit number)
12109173162792642280…14724200591055523839
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
1.210 × 10⁹⁷(98-digit number)
12109173162792642280…14724200591055523839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.421 × 10⁹⁷(98-digit number)
24218346325585284561…29448401182111047679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.843 × 10⁹⁷(98-digit number)
48436692651170569122…58896802364222095359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.687 × 10⁹⁷(98-digit number)
96873385302341138244…17793604728444190719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.937 × 10⁹⁸(99-digit number)
19374677060468227648…35587209456888381439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.874 × 10⁹⁸(99-digit number)
38749354120936455297…71174418913776762879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.749 × 10⁹⁸(99-digit number)
77498708241872910595…42348837827553525759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.549 × 10⁹⁹(100-digit number)
15499741648374582119…84697675655107051519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.099 × 10⁹⁹(100-digit number)
30999483296749164238…69395351310214103039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.199 × 10⁹⁹(100-digit number)
61998966593498328476…38790702620428206079
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:57,730,702 XPM·at block #6,810,825 · updates every 60s
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