Block #238,060

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2013, 9:03:00 AM · Difficulty 9.9513 · 6,560,833 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
abc420ebddb82b6aa8b4a7c5cbeefc6ff6fdd37fc86a78cf35476fbf6e12bec6

Height

#238,060

Difficulty

9.951268

Transactions

1

Size

1.98 KB

Version

2

Bits

09f3864b

Nonce

131,313

Timestamp

11/1/2013, 9:03:00 AM

Confirmations

6,560,833

Merkle Root

e9650714e03ce9b85423099acd149d29c52d804ef910cbb7fd53dff1b2aa1dad
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.

2.281 × 10⁹⁸(99-digit number)
22814022877096173688…80547778161356443079
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
2.281 × 10⁹⁸(99-digit number)
22814022877096173688…80547778161356443079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.562 × 10⁹⁸(99-digit number)
45628045754192347377…61095556322712886159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.125 × 10⁹⁸(99-digit number)
91256091508384694755…22191112645425772319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.825 × 10⁹⁹(100-digit number)
18251218301676938951…44382225290851544639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.650 × 10⁹⁹(100-digit number)
36502436603353877902…88764450581703089279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.300 × 10⁹⁹(100-digit number)
73004873206707755804…77528901163406178559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.460 × 10¹⁰⁰(101-digit number)
14600974641341551160…55057802326812357119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.920 × 10¹⁰⁰(101-digit number)
29201949282683102321…10115604653624714239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.840 × 10¹⁰⁰(101-digit number)
58403898565366204643…20231209307249428479
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,635,184 XPM·at block #6,798,892 · updates every 60s
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