Block #265,210

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/19/2013, 8:38:09 AM · Difficulty 9.9632 · 6,537,358 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
2843a8b171545289a5c946de9e12b2bcd41da7ef3f76d993759f418409287ffa

Height

#265,210

Difficulty

9.963187

Transactions

4

Size

24.14 KB

Version

2

Bits

09f6936b

Nonce

27,076

Timestamp

11/19/2013, 8:38:09 AM

Confirmations

6,537,358

Merkle Root

35c0af56cb9592301d6e1ea473699754cecf714dcd41f489649c665f93eceabb
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.

7.858 × 10⁹⁵(96-digit number)
78584681996743361796…82807745832746534921
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
7.858 × 10⁹⁵(96-digit number)
78584681996743361796…82807745832746534921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.571 × 10⁹⁶(97-digit number)
15716936399348672359…65615491665493069841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.143 × 10⁹⁶(97-digit number)
31433872798697344718…31230983330986139681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.286 × 10⁹⁶(97-digit number)
62867745597394689437…62461966661972279361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.257 × 10⁹⁷(98-digit number)
12573549119478937887…24923933323944558721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.514 × 10⁹⁷(98-digit number)
25147098238957875775…49847866647889117441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.029 × 10⁹⁷(98-digit number)
50294196477915751550…99695733295778234881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.005 × 10⁹⁸(99-digit number)
10058839295583150310…99391466591556469761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.011 × 10⁹⁸(99-digit number)
20117678591166300620…98782933183112939521
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:57,664,559 XPM·at block #6,802,567 · updates every 60s
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