Block #387,187

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/2/2014, 10:50:26 PM · Difficulty 10.4161 · 6,422,601 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c9cb6526b31dfa15d57c91db53c2b93c32a1a83bf57da758fdad3b6a1d4daf88

Height

#387,187

Difficulty

10.416142

Transactions

2

Size

434 B

Version

2

Bits

0a6a8845

Nonce

11,987

Timestamp

2/2/2014, 10:50:26 PM

Confirmations

6,422,601

Merkle Root

fc9ee43725db0444657c5cdde59f3762d2925709b41e3214f509eeb75da40ca6
Transactions (2)
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.

2.105 × 10¹⁰⁰(101-digit number)
21051205069750766424…06175357277027123199
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
2.105 × 10¹⁰⁰(101-digit number)
21051205069750766424…06175357277027123199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.210 × 10¹⁰⁰(101-digit number)
42102410139501532849…12350714554054246399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.420 × 10¹⁰⁰(101-digit number)
84204820279003065698…24701429108108492799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.684 × 10¹⁰¹(102-digit number)
16840964055800613139…49402858216216985599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.368 × 10¹⁰¹(102-digit number)
33681928111601226279…98805716432433971199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
6.736 × 10¹⁰¹(102-digit number)
67363856223202452558…97611432864867942399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.347 × 10¹⁰²(103-digit number)
13472771244640490511…95222865729735884799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.694 × 10¹⁰²(103-digit number)
26945542489280981023…90445731459471769599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.389 × 10¹⁰²(103-digit number)
53891084978561962047…80891462918943539199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.077 × 10¹⁰³(104-digit number)
10778216995712392409…61782925837887078399
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:57,722,384 XPM·at block #6,809,787 · updates every 60s
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