Block #379,932

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/28/2014, 8:53:36 PM · Difficulty 10.4206 · 6,430,248 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
795015cb98cb67ce79f87757be0e4e232a122e1c2983bbb7788762aa9d2421cc

Height

#379,932

Difficulty

10.420557

Transactions

3

Size

950 B

Version

2

Bits

0a6ba9a3

Nonce

159,637

Timestamp

1/28/2014, 8:53:36 PM

Confirmations

6,430,248

Merkle Root

2feeff6226a6a79667c648e5b55d9a49c8e5c2554f84c1f40ff9949abafe1844
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.

3.628 × 10⁹⁶(97-digit number)
36280445321084202807…74351876961737868699
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
3.628 × 10⁹⁶(97-digit number)
36280445321084202807…74351876961737868699
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.256 × 10⁹⁶(97-digit number)
72560890642168405615…48703753923475737399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.451 × 10⁹⁷(98-digit number)
14512178128433681123…97407507846951474799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.902 × 10⁹⁷(98-digit number)
29024356256867362246…94815015693902949599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
5.804 × 10⁹⁷(98-digit number)
58048712513734724492…89630031387805899199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.160 × 10⁹⁸(99-digit number)
11609742502746944898…79260062775611798399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.321 × 10⁹⁸(99-digit number)
23219485005493889797…58520125551223596799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.643 × 10⁹⁸(99-digit number)
46438970010987779594…17040251102447193599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.287 × 10⁹⁸(99-digit number)
92877940021975559188…34080502204894387199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.857 × 10⁹⁹(100-digit number)
18575588004395111837…68161004409788774399
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:57,725,509 XPM·at block #6,810,179 · updates every 60s
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