Block #202,487

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/10/2013, 6:16:19 AM · Difficulty 9.8952 · 6,608,435 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
ae3c5b1428c1434417bb6a504e72d619031825c31c0e49105b46795144ba8038

Height

#202,487

Difficulty

9.895242

Transactions

1

Size

3.54 KB

Version

2

Bits

09e52e8f

Nonce

1,164,758,277

Timestamp

10/10/2013, 6:16:19 AM

Confirmations

6,608,435

Merkle Root

6d634e6074298cdc630e2ac19ecbf130a5ed13e6c9332a31990a44ebec02b958
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.

1.185 × 10⁹⁵(96-digit number)
11856531274143233596…89719322974043185921
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
1.185 × 10⁹⁵(96-digit number)
11856531274143233596…89719322974043185921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.371 × 10⁹⁵(96-digit number)
23713062548286467192…79438645948086371841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.742 × 10⁹⁵(96-digit number)
47426125096572934385…58877291896172743681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.485 × 10⁹⁵(96-digit number)
94852250193145868771…17754583792345487361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.897 × 10⁹⁶(97-digit number)
18970450038629173754…35509167584690974721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.794 × 10⁹⁶(97-digit number)
37940900077258347508…71018335169381949441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.588 × 10⁹⁶(97-digit number)
75881800154516695017…42036670338763898881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.517 × 10⁹⁷(98-digit number)
15176360030903339003…84073340677527797761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.035 × 10⁹⁷(98-digit number)
30352720061806678007…68146681355055595521
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:57,731,478 XPM·at block #6,810,921 · updates every 60s
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