Block #367,627

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/20/2014, 5:30:21 AM · Difficulty 10.4332 · 6,427,247 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
b98fa50981833e3a25f5f7198ee3384ca85c2a08007e102285fc3954e3ec3449

Height

#367,627

Difficulty

10.433161

Transactions

3

Size

955 B

Version

2

Bits

0a6ee39c

Nonce

14,282

Timestamp

1/20/2014, 5:30:21 AM

Confirmations

6,427,247

Merkle Root

68fd66682929b1ddd18589784a9511961d73a7c065014bc7d79488c62643f557
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.

1.447 × 10¹⁰²(103-digit number)
14473790869387570443…75403191994957168639
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
1.447 × 10¹⁰²(103-digit number)
14473790869387570443…75403191994957168639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.894 × 10¹⁰²(103-digit number)
28947581738775140886…50806383989914337279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.789 × 10¹⁰²(103-digit number)
57895163477550281772…01612767979828674559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.157 × 10¹⁰³(104-digit number)
11579032695510056354…03225535959657349119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.315 × 10¹⁰³(104-digit number)
23158065391020112708…06451071919314698239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.631 × 10¹⁰³(104-digit number)
46316130782040225417…12902143838629396479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
9.263 × 10¹⁰³(104-digit number)
92632261564080450835…25804287677258792959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.852 × 10¹⁰⁴(105-digit number)
18526452312816090167…51608575354517585919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.705 × 10¹⁰⁴(105-digit number)
37052904625632180334…03217150709035171839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
7.410 × 10¹⁰⁴(105-digit number)
74105809251264360668…06434301418070343679
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:57,603,025 XPM·at block #6,794,873 · updates every 60s
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