Block #484,015

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/10/2014, 8:52:53 AM · Difficulty 10.5756 · 6,332,740 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f42c561aeb2b82d0c3835675b03743722033120d9cbca92770e6e7fcdebd4e95

Height

#484,015

Difficulty

10.575610

Transactions

1

Size

801 B

Version

2

Bits

0a935b2a

Nonce

21,691

Timestamp

4/10/2014, 8:52:53 AM

Confirmations

6,332,740

Merkle Root

d6ec467d0924bedeb902e708c50da647b419b7b82e82d38550860e1235503fcc
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.

2.264 × 10¹⁰⁰(101-digit number)
22649307731717534647…92464640869989555419
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
2.264 × 10¹⁰⁰(101-digit number)
22649307731717534647…92464640869989555419
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.529 × 10¹⁰⁰(101-digit number)
45298615463435069295…84929281739979110839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.059 × 10¹⁰⁰(101-digit number)
90597230926870138590…69858563479958221679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.811 × 10¹⁰¹(102-digit number)
18119446185374027718…39717126959916443359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.623 × 10¹⁰¹(102-digit number)
36238892370748055436…79434253919832886719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.247 × 10¹⁰¹(102-digit number)
72477784741496110872…58868507839665773439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.449 × 10¹⁰²(103-digit number)
14495556948299222174…17737015679331546879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.899 × 10¹⁰²(103-digit number)
28991113896598444349…35474031358663093759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.798 × 10¹⁰²(103-digit number)
57982227793196888698…70948062717326187519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.159 × 10¹⁰³(104-digit number)
11596445558639377739…41896125434652375039
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:57,778,071 XPM·at block #6,816,754 · updates every 60s
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