Block #1,454,478

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/13/2016, 2:05:12 PM · Difficulty 10.7203 · 5,362,732 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
2d0423a276fe6322e5e13c0a4275ead45a4a4e269069f2acf8b692698f6ebe39

Height

#1,454,478

Difficulty

10.720288

Transactions

2

Size

1.11 KB

Version

2

Bits

0ab864c4

Nonce

1,268,199,172

Timestamp

2/13/2016, 2:05:12 PM

Confirmations

5,362,732

Merkle Root

511e1d509b5241e34b13cf15abcc532754aa1a39546acf2e504ee0f93b9be721
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.

4.716 × 10⁹⁴(95-digit number)
47169511346688940822…07038846866473982879
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
4.716 × 10⁹⁴(95-digit number)
47169511346688940822…07038846866473982879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.433 × 10⁹⁴(95-digit number)
94339022693377881644…14077693732947965759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.886 × 10⁹⁵(96-digit number)
18867804538675576328…28155387465895931519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.773 × 10⁹⁵(96-digit number)
37735609077351152657…56310774931791863039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.547 × 10⁹⁵(96-digit number)
75471218154702305315…12621549863583726079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.509 × 10⁹⁶(97-digit number)
15094243630940461063…25243099727167452159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.018 × 10⁹⁶(97-digit number)
30188487261880922126…50486199454334904319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.037 × 10⁹⁶(97-digit number)
60376974523761844252…00972398908669808639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.207 × 10⁹⁷(98-digit number)
12075394904752368850…01944797817339617279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.415 × 10⁹⁷(98-digit number)
24150789809504737700…03889595634679234559
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:57,781,719 XPM·at block #6,817,209 · updates every 60s
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