Block #388,231

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/3/2014, 4:04:00 PM · Difficulty 10.4179 · 6,422,448 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d7f6563b152a9388afad8387434f36bf367c0c7348d5a7afb403c67e45e05116

Height

#388,231

Difficulty

10.417889

Transactions

2

Size

392 B

Version

2

Bits

0a6afac1

Nonce

149,299

Timestamp

2/3/2014, 4:04:00 PM

Confirmations

6,422,448

Merkle Root

5f4cb179a4a1749f7f3d1dc0df796b25b623509f8cbea09e37fc2032fbfa4a6a
Transactions (2)
1 in → 1 out9.2100 XPM110 B
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.

1.986 × 10⁹⁶(97-digit number)
19862989352586326328…25462143161695168359
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
1.986 × 10⁹⁶(97-digit number)
19862989352586326328…25462143161695168359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.972 × 10⁹⁶(97-digit number)
39725978705172652657…50924286323390336719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.945 × 10⁹⁶(97-digit number)
79451957410345305315…01848572646780673439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.589 × 10⁹⁷(98-digit number)
15890391482069061063…03697145293561346879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.178 × 10⁹⁷(98-digit number)
31780782964138122126…07394290587122693759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.356 × 10⁹⁷(98-digit number)
63561565928276244252…14788581174245387519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.271 × 10⁹⁸(99-digit number)
12712313185655248850…29577162348490775039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.542 × 10⁹⁸(99-digit number)
25424626371310497700…59154324696981550079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.084 × 10⁹⁸(99-digit number)
50849252742620995401…18308649393963100159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.016 × 10⁹⁹(100-digit number)
10169850548524199080…36617298787926200319
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:57,729,524 XPM·at block #6,810,678 · updates every 60s
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