Block #206,550

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/12/2013, 9:12:50 PM · Difficulty 9.9013 · 6,590,264 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1e350970402c20db2ef93ecd5b2052386d1dc67e0b4d3c81a6206ab7e8f496e9

Height

#206,550

Difficulty

9.901349

Transactions

2

Size

426 B

Version

2

Bits

09e6bed5

Nonce

526,780

Timestamp

10/12/2013, 9:12:50 PM

Confirmations

6,590,264

Merkle Root

9635acd80364cc07dec52daff70cfcb1006a4eede4c5ab2b128ff3b795aa4689
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.

7.457 × 10⁹⁴(95-digit number)
74579086707446321198…17447148988534442281
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
7.457 × 10⁹⁴(95-digit number)
74579086707446321198…17447148988534442281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.491 × 10⁹⁵(96-digit number)
14915817341489264239…34894297977068884561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.983 × 10⁹⁵(96-digit number)
29831634682978528479…69788595954137769121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.966 × 10⁹⁵(96-digit number)
59663269365957056959…39577191908275538241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.193 × 10⁹⁶(97-digit number)
11932653873191411391…79154383816551076481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.386 × 10⁹⁶(97-digit number)
23865307746382822783…58308767633102152961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.773 × 10⁹⁶(97-digit number)
47730615492765645567…16617535266204305921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.546 × 10⁹⁶(97-digit number)
95461230985531291134…33235070532408611841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.909 × 10⁹⁷(98-digit number)
19092246197106258226…66470141064817223681
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:57,618,520 XPM·at block #6,796,813 · updates every 60s
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