Block #24,337

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/12/2013, 10:44:01 PM · Difficulty 7.9651 · 6,802,604 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
76c3254e0f88ebf7a054b8fffaa8dee1123695a18664e9098dddd000d9c5c2bb

Height

#24,337

Difficulty

7.965125

Transactions

2

Size

17.74 KB

Version

2

Bits

07f71273

Nonce

33

Timestamp

7/12/2013, 10:44:01 PM

Confirmations

6,802,604

Merkle Root

cfa1f960402a99c15e7f1155478caadd6643750126c1eaf177419c809d2610ff
Transactions (2)
1 in → 1 out15.9200 XPM108 B
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.

8.843 × 10¹¹²(113-digit number)
88430247808032135782…93191451524548122919
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
8.843 × 10¹¹²(113-digit number)
88430247808032135782…93191451524548122919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.768 × 10¹¹³(114-digit number)
17686049561606427156…86382903049096245839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.537 × 10¹¹³(114-digit number)
35372099123212854312…72765806098192491679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.074 × 10¹¹³(114-digit number)
70744198246425708625…45531612196384983359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.414 × 10¹¹⁴(115-digit number)
14148839649285141725…91063224392769966719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.829 × 10¹¹⁴(115-digit number)
28297679298570283450…82126448785539933439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.659 × 10¹¹⁴(115-digit number)
56595358597140566900…64252897571079866879
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 consecutive prime numbers forming a Cunningham Chain of the First 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 7

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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,859,702 XPM·at block #6,826,940 · updates every 60s
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