Block #373,448

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 1/24/2014, 7:51:09 AM · Difficulty 10.4249 · 6,442,772 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
91a40693f3578da48ac876965b7186a2b2cb31384ae218df78f3bc6e0aeefce7

Height

#373,448

Difficulty

10.424913

Transactions

1

Size

903 B

Version

2

Bits

0a6cc718

Nonce

104,847

Timestamp

1/24/2014, 7:51:09 AM

Confirmations

6,442,772

Merkle Root

aef3b1b83cd1719ac0039e73837efec982cd61c7822014e451ea694c55445f2b
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.

7.918 × 10⁹⁹(100-digit number)
79187455798071220203…49828337164642864379
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
7.918 × 10⁹⁹(100-digit number)
79187455798071220203…49828337164642864379
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.583 × 10¹⁰⁰(101-digit number)
15837491159614244040…99656674329285728759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.167 × 10¹⁰⁰(101-digit number)
31674982319228488081…99313348658571457519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.334 × 10¹⁰⁰(101-digit number)
63349964638456976162…98626697317142915039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.266 × 10¹⁰¹(102-digit number)
12669992927691395232…97253394634285830079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.533 × 10¹⁰¹(102-digit number)
25339985855382790465…94506789268571660159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.067 × 10¹⁰¹(102-digit number)
50679971710765580930…89013578537143320319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.013 × 10¹⁰²(103-digit number)
10135994342153116186…78027157074286640639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.027 × 10¹⁰²(103-digit number)
20271988684306232372…56054314148573281279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.054 × 10¹⁰²(103-digit number)
40543977368612464744…12108628297146562559
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,773,889 XPM·at block #6,816,219 · updates every 60s
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