Block #207,224

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/13/2013, 8:06:33 AM · Difficulty 9.9018 · 6,605,777 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
493cb9facb1b2c7b1ac0a798d08222f42a28ecd17fbf8142adfdc090db7e64ca

Height

#207,224

Difficulty

9.901772

Transactions

3

Size

653 B

Version

2

Bits

09e6da84

Nonce

22,717

Timestamp

10/13/2013, 8:06:33 AM

Confirmations

6,605,777

Merkle Root

3a990d590d1116cfc0b6cb67fd4753d9c8a95dadccf06a90587b6ebb91db42e9
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.

2.266 × 10⁹⁴(95-digit number)
22665956655034465746…70286491305913361661
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
2.266 × 10⁹⁴(95-digit number)
22665956655034465746…70286491305913361661
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.533 × 10⁹⁴(95-digit number)
45331913310068931493…40572982611826723321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.066 × 10⁹⁴(95-digit number)
90663826620137862986…81145965223653446641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.813 × 10⁹⁵(96-digit number)
18132765324027572597…62291930447306893281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.626 × 10⁹⁵(96-digit number)
36265530648055145194…24583860894613786561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.253 × 10⁹⁵(96-digit number)
72531061296110290389…49167721789227573121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.450 × 10⁹⁶(97-digit number)
14506212259222058077…98335443578455146241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.901 × 10⁹⁶(97-digit number)
29012424518444116155…96670887156910292481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.802 × 10⁹⁶(97-digit number)
58024849036888232311…93341774313820584961
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:57,748,048 XPM·at block #6,813,000 · updates every 60s
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