Block #203,482

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/10/2013, 9:07:53 PM · Difficulty 9.8975 · 6,623,875 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
27216ff03ce34c4f8c70bf61f2fe9e10086e1f74ee78ceaba8b9884517b0f8ad

Height

#203,482

Difficulty

9.897503

Transactions

2

Size

574 B

Version

2

Bits

09e5c2ca

Nonce

63,692

Timestamp

10/10/2013, 9:07:53 PM

Confirmations

6,623,875

Merkle Root

6019de4c4e03418b83d18896847f129fc66ff44570cb2e8715d5e96ec4ccf665
Transactions (2)
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.

5.424 × 10⁹⁷(98-digit number)
54244348114554968479…40678393398448223361
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
5.424 × 10⁹⁷(98-digit number)
54244348114554968479…40678393398448223361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.084 × 10⁹⁸(99-digit number)
10848869622910993695…81356786796896446721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.169 × 10⁹⁸(99-digit number)
21697739245821987391…62713573593792893441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.339 × 10⁹⁸(99-digit number)
43395478491643974783…25427147187585786881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.679 × 10⁹⁸(99-digit number)
86790956983287949567…50854294375171573761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.735 × 10⁹⁹(100-digit number)
17358191396657589913…01708588750343147521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.471 × 10⁹⁹(100-digit number)
34716382793315179826…03417177500686295041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.943 × 10⁹⁹(100-digit number)
69432765586630359653…06834355001372590081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.388 × 10¹⁰⁰(101-digit number)
13886553117326071930…13668710002745180161
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:57,862,955 XPM·at block #6,827,356 · updates every 60s
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