Block #228,955

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/26/2013, 8:49:32 PM · Difficulty 9.9381 · 6,598,277 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
3a2fc4024a8bceb7313d32404aa4b844ebbe106b22d08ac3d49c2505f86fba0b

Height

#228,955

Difficulty

9.938061

Transactions

3

Size

1.76 KB

Version

2

Bits

09f024c4

Nonce

44,720

Timestamp

10/26/2013, 8:49:32 PM

Confirmations

6,598,277

Merkle Root

5859d5c9ce72c1812b16d3e95ed13509822092d66777e5827424af1751b2f160
Transactions (3)
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.

8.867 × 10⁹⁵(96-digit number)
88673387102502351763…15974526160797711359
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
8.867 × 10⁹⁵(96-digit number)
88673387102502351763…15974526160797711359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.773 × 10⁹⁶(97-digit number)
17734677420500470352…31949052321595422719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.546 × 10⁹⁶(97-digit number)
35469354841000940705…63898104643190845439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.093 × 10⁹⁶(97-digit number)
70938709682001881410…27796209286381690879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.418 × 10⁹⁷(98-digit number)
14187741936400376282…55592418572763381759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.837 × 10⁹⁷(98-digit number)
28375483872800752564…11184837145526763519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.675 × 10⁹⁷(98-digit number)
56750967745601505128…22369674291053527039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.135 × 10⁹⁸(99-digit number)
11350193549120301025…44739348582107054079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.270 × 10⁹⁸(99-digit number)
22700387098240602051…89478697164214108159
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:57,861,956 XPM·at block #6,827,231 · updates every 60s
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