Block #387,487

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/3/2014, 4:24:54 AM · Difficulty 10.4125 · 6,416,574 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
69415d4856876a4b9c0dc547b47e0fd147bd8d0eb9f3b263e005c5198d88360f

Height

#387,487

Difficulty

10.412513

Transactions

3

Size

801 B

Version

2

Bits

0a699a72

Nonce

917,485

Timestamp

2/3/2014, 4:24:54 AM

Confirmations

6,416,574

Merkle Root

591640cdca1b273e4400c6975aede2ad8660c2950d0d9320fe1e2ac90112640d
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.

7.264 × 10⁹⁵(96-digit number)
72640053362773342345…17845860139075736079
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
7.264 × 10⁹⁵(96-digit number)
72640053362773342345…17845860139075736079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.452 × 10⁹⁶(97-digit number)
14528010672554668469…35691720278151472159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.905 × 10⁹⁶(97-digit number)
29056021345109336938…71383440556302944319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.811 × 10⁹⁶(97-digit number)
58112042690218673876…42766881112605888639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.162 × 10⁹⁷(98-digit number)
11622408538043734775…85533762225211777279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.324 × 10⁹⁷(98-digit number)
23244817076087469550…71067524450423554559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.648 × 10⁹⁷(98-digit number)
46489634152174939101…42135048900847109119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
9.297 × 10⁹⁷(98-digit number)
92979268304349878202…84270097801694218239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.859 × 10⁹⁸(99-digit number)
18595853660869975640…68540195603388436479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
3.719 × 10⁹⁸(99-digit number)
37191707321739951280…37080391206776872959
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:57,676,544 XPM·at block #6,804,060 · updates every 60s
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