Block #201,387

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 10/9/2013, 3:04:49 PM · Difficulty 9.8912 · 6,600,074 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
5f57666e972efce5611e0af083d1fa6cd94d0ec587ca656e294eae19d40672d8

Height

#201,387

Difficulty

9.891216

Transactions

1

Size

3.57 KB

Version

2

Bits

09e426b3

Nonce

1,164,748,175

Timestamp

10/9/2013, 3:04:49 PM

Confirmations

6,600,074

Merkle Root

4875701b592fa0e16be5c6884de16eeb5f93e8fbc59eb3973ec7728b68a3c243
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.

9.158 × 10⁹⁰(91-digit number)
91588233928394606687…55483489706815626959
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
9.158 × 10⁹⁰(91-digit number)
91588233928394606687…55483489706815626959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.831 × 10⁹¹(92-digit number)
18317646785678921337…10966979413631253919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.663 × 10⁹¹(92-digit number)
36635293571357842675…21933958827262507839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.327 × 10⁹¹(92-digit number)
73270587142715685350…43867917654525015679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.465 × 10⁹²(93-digit number)
14654117428543137070…87735835309050031359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.930 × 10⁹²(93-digit number)
29308234857086274140…75471670618100062719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.861 × 10⁹²(93-digit number)
58616469714172548280…50943341236200125439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.172 × 10⁹³(94-digit number)
11723293942834509656…01886682472400250879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.344 × 10⁹³(94-digit number)
23446587885669019312…03773364944800501759
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:57,655,762 XPM·at block #6,801,460 · updates every 60s
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