Block #767,963

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 10/14/2014, 5:48:30 PM · Difficulty 10.9792 · 6,035,524 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
1ac84585d992682c9836e7e2bc2680a1e03b7086e665303ff3cd215fb55bbc87

Height

#767,963

Difficulty

10.979207

Transactions

5

Size

29.41 KB

Version

2

Bits

0afaad57

Nonce

558,324,232

Timestamp

10/14/2014, 5:48:30 PM

Confirmations

6,035,524

Merkle Root

05310fa306d4ebf1ba1fd53d8ff2206a7ba5274885d208b2e528969a638d0a42
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.

5.236 × 10⁹⁶(97-digit number)
52366348098627393525…23061194502008977921
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
5.236 × 10⁹⁶(97-digit number)
52366348098627393525…23061194502008977921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.047 × 10⁹⁷(98-digit number)
10473269619725478705…46122389004017955841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.094 × 10⁹⁷(98-digit number)
20946539239450957410…92244778008035911681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.189 × 10⁹⁷(98-digit number)
41893078478901914820…84489556016071823361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
8.378 × 10⁹⁷(98-digit number)
83786156957803829640…68979112032143646721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.675 × 10⁹⁸(99-digit number)
16757231391560765928…37958224064287293441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.351 × 10⁹⁸(99-digit number)
33514462783121531856…75916448128574586881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
6.702 × 10⁹⁸(99-digit number)
67028925566243063712…51832896257149173761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.340 × 10⁹⁹(100-digit number)
13405785113248612742…03665792514298347521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.681 × 10⁹⁹(100-digit number)
26811570226497225484…07331585028596695041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
5.362 × 10⁹⁹(100-digit number)
53623140452994450969…14663170057193390081
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,671,927 XPM·at block #6,803,486 · updates every 60s
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