Block #232,600

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/29/2013, 5:21:48 AM · Difficulty 9.9412 · 6,598,001 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a36ba6bcf66cd8e2e41106185738fc98a69f7508986711eb76bafc2b80db5c82

Height

#232,600

Difficulty

9.941246

Transactions

1

Size

1.58 KB

Version

2

Bits

09f0f578

Nonce

38,035

Timestamp

10/29/2013, 5:21:48 AM

Confirmations

6,598,001

Merkle Root

3bf608687f150a3c623944a6b1a4fe44eac5b7e32f15bced17514900b003106c
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.

2.776 × 10⁹¹(92-digit number)
27768142559583235112…73225224278479254081
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
2.776 × 10⁹¹(92-digit number)
27768142559583235112…73225224278479254081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.553 × 10⁹¹(92-digit number)
55536285119166470225…46450448556958508161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.110 × 10⁹²(93-digit number)
11107257023833294045…92900897113917016321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.221 × 10⁹²(93-digit number)
22214514047666588090…85801794227834032641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.442 × 10⁹²(93-digit number)
44429028095333176180…71603588455668065281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
8.885 × 10⁹²(93-digit number)
88858056190666352361…43207176911336130561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.777 × 10⁹³(94-digit number)
17771611238133270472…86414353822672261121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.554 × 10⁹³(94-digit number)
35543222476266540944…72828707645344522241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.108 × 10⁹³(94-digit number)
71086444952533081888…45657415290689044481
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,888,930 XPM·at block #6,830,600 · updates every 60s
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