Block #200,930

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 7:52:05 AM · Difficulty 9.8907 · 6,608,503 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f98fa3bf1ce29ddd48a40b29cd823cc4eb083e9f489dcf6585f06a73e854cd46

Height

#200,930

Difficulty

9.890665

Transactions

4

Size

1.27 KB

Version

2

Bits

09e402a3

Nonce

5,621

Timestamp

10/9/2013, 7:52:05 AM

Confirmations

6,608,503

Merkle Root

bfcf313b423b536268c4525bd97faee9a11c35cc9c5e0233f9bac5bb687f4ad8
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.

1.984 × 10⁹⁵(96-digit number)
19846385198423364972…19305806433233114879
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
1.984 × 10⁹⁵(96-digit number)
19846385198423364972…19305806433233114879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.969 × 10⁹⁵(96-digit number)
39692770396846729945…38611612866466229759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
7.938 × 10⁹⁵(96-digit number)
79385540793693459890…77223225732932459519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.587 × 10⁹⁶(97-digit number)
15877108158738691978…54446451465864919039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.175 × 10⁹⁶(97-digit number)
31754216317477383956…08892902931729838079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.350 × 10⁹⁶(97-digit number)
63508432634954767912…17785805863459676159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.270 × 10⁹⁷(98-digit number)
12701686526990953582…35571611726919352319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.540 × 10⁹⁷(98-digit number)
25403373053981907164…71143223453838704639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.080 × 10⁹⁷(98-digit number)
50806746107963814329…42286446907677409279
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:57,719,533 XPM·at block #6,809,432 · updates every 60s
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