Block #93,492

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/2/2013, 11:19:30 AM · Difficulty 9.1970 · 6,722,480 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e18dbc5e54fa029a60d0a7f59d42afa8bf25ee80b7354506280ca90f9ae64882

Height

#93,492

Difficulty

9.197049

Transactions

5

Size

1.59 KB

Version

2

Bits

093271d6

Nonce

7,562

Timestamp

8/2/2013, 11:19:30 AM

Confirmations

6,722,480

Merkle Root

31c85f31283dc4c94a2185b3496ea505aa799f0811feb1cdb94d5f7dcb60892e
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.

3.845 × 10¹⁰⁵(106-digit number)
38450446813864621419…86669523325723596319
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
3.845 × 10¹⁰⁵(106-digit number)
38450446813864621419…86669523325723596319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
7.690 × 10¹⁰⁵(106-digit number)
76900893627729242838…73339046651447192639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.538 × 10¹⁰⁶(107-digit number)
15380178725545848567…46678093302894385279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.076 × 10¹⁰⁶(107-digit number)
30760357451091697135…93356186605788770559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
6.152 × 10¹⁰⁶(107-digit number)
61520714902183394270…86712373211577541119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.230 × 10¹⁰⁷(108-digit number)
12304142980436678854…73424746423155082239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
2.460 × 10¹⁰⁷(108-digit number)
24608285960873357708…46849492846310164479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
4.921 × 10¹⁰⁷(108-digit number)
49216571921746715416…93698985692620328959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
9.843 × 10¹⁰⁷(108-digit number)
98433143843493430832…87397971385240657919
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 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 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,771,889 XPM·at block #6,815,971 · updates every 60s
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