Block #447,055

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 3/17/2014, 12:04:32 AM · Difficulty 10.3608 · 6,363,881 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3722a6bce1814f82287896573ed4493f686401a88f56207d7d6cf6bc47d047e6

Height

#447,055

Difficulty

10.360834

Transactions

2

Size

1.70 KB

Version

2

Bits

0a5c5fa5

Nonce

68,810

Timestamp

3/17/2014, 12:04:32 AM

Confirmations

6,363,881

Merkle Root

4c50a1c07037f709e7e4c7f75108df8e4da9595b554d296655ae4b9bd6b514b8
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.

2.447 × 10⁹⁷(98-digit number)
24478340679006720889…70094650358280722539
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
2.447 × 10⁹⁷(98-digit number)
24478340679006720889…70094650358280722539
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.895 × 10⁹⁷(98-digit number)
48956681358013441778…40189300716561445079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.791 × 10⁹⁷(98-digit number)
97913362716026883556…80378601433122890159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.958 × 10⁹⁸(99-digit number)
19582672543205376711…60757202866245780319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.916 × 10⁹⁸(99-digit number)
39165345086410753422…21514405732491560639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.833 × 10⁹⁸(99-digit number)
78330690172821506845…43028811464983121279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.566 × 10⁹⁹(100-digit number)
15666138034564301369…86057622929966242559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.133 × 10⁹⁹(100-digit number)
31332276069128602738…72115245859932485119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.266 × 10⁹⁹(100-digit number)
62664552138257205476…44230491719864970239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.253 × 10¹⁰⁰(101-digit number)
12532910427651441095…88460983439729940479
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:57,731,592 XPM·at block #6,810,935 · updates every 60s
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