Block #373,137

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 2:48:23 AM · Difficulty 10.4244 · 6,444,808 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
fd112f450e1c2b9788655a1ca35b7ad9a59b37e46be49ecd199aa096b63294d2

Height

#373,137

Difficulty

10.424371

Transactions

4

Size

3.70 KB

Version

2

Bits

0a6ca38c

Nonce

136

Timestamp

1/24/2014, 2:48:23 AM

Confirmations

6,444,808

Merkle Root

144b60afdd8ddb157e7ccb4196a000a9d683074f351f86ee46b78bdcb109bc92
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.

8.224 × 10⁹⁹(100-digit number)
82247091708880860535…78261631174919664639
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
8.224 × 10⁹⁹(100-digit number)
82247091708880860535…78261631174919664639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.644 × 10¹⁰⁰(101-digit number)
16449418341776172107…56523262349839329279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.289 × 10¹⁰⁰(101-digit number)
32898836683552344214…13046524699678658559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.579 × 10¹⁰⁰(101-digit number)
65797673367104688428…26093049399357317119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.315 × 10¹⁰¹(102-digit number)
13159534673420937685…52186098798714634239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.631 × 10¹⁰¹(102-digit number)
26319069346841875371…04372197597429268479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.263 × 10¹⁰¹(102-digit number)
52638138693683750742…08744395194858536959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.052 × 10¹⁰²(103-digit number)
10527627738736750148…17488790389717073919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.105 × 10¹⁰²(103-digit number)
21055255477473500297…34977580779434147839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.211 × 10¹⁰²(103-digit number)
42110510954947000594…69955161558868295679
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:57,787,627 XPM·at block #6,817,944 · updates every 60s
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