Block #371,998

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/23/2014, 7:01:57 AM · Difficulty 10.4297 · 6,464,760 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
6227c8b288d488d69797877699296a5a852462f2d27d744d504c5f6d334c4b5b

Height

#371,998

Difficulty

10.429701

Transactions

4

Size

1.15 KB

Version

2

Bits

0a6e00dd

Nonce

75,481

Timestamp

1/23/2014, 7:01:57 AM

Confirmations

6,464,760

Merkle Root

e34b03c1ed4a019c002c9806ba7cb18427dbdc45716c669b06b8899ddcdb8ab3
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.

2.633 × 10⁹⁹(100-digit number)
26339877765859644103…34605807766428493439
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
2.633 × 10⁹⁹(100-digit number)
26339877765859644103…34605807766428493439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.267 × 10⁹⁹(100-digit number)
52679755531719288207…69211615532856986879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.053 × 10¹⁰⁰(101-digit number)
10535951106343857641…38423231065713973759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.107 × 10¹⁰⁰(101-digit number)
21071902212687715282…76846462131427947519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.214 × 10¹⁰⁰(101-digit number)
42143804425375430565…53692924262855895039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.428 × 10¹⁰⁰(101-digit number)
84287608850750861131…07385848525711790079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.685 × 10¹⁰¹(102-digit number)
16857521770150172226…14771697051423580159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.371 × 10¹⁰¹(102-digit number)
33715043540300344452…29543394102847160319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.743 × 10¹⁰¹(102-digit number)
67430087080600688905…59086788205694320639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.348 × 10¹⁰²(103-digit number)
13486017416120137781…18173576411388641279
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:57,938,346 XPM·at block #6,836,757 · updates every 60s
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