Block #93,384

1CCLength 9★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 8/2/2013, 9:40:31 AM · Difficulty 9.1954 · 6,733,960 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e336cc9f64dadaac9fd8995ca5c25ac14cba50cf27be2dde892855f38d240354

Height

#93,384

Difficulty

9.195392

Transactions

4

Size

1.66 KB

Version

2

Bits

09320530

Nonce

11,507

Timestamp

8/2/2013, 9:40:31 AM

Confirmations

6,733,960

Merkle Root

01915eb46d1b884686060a5e738f34ac4aabac0a321e5e31f0e4f41f2aa4b0d9
Transactions (4)
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.

6.963 × 10¹¹⁶(117-digit number)
69638769201057533768…71061813089705207659
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
6.963 × 10¹¹⁶(117-digit number)
69638769201057533768…71061813089705207659
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.392 × 10¹¹⁷(118-digit number)
13927753840211506753…42123626179410415319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.785 × 10¹¹⁷(118-digit number)
27855507680423013507…84247252358820830639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
5.571 × 10¹¹⁷(118-digit number)
55711015360846027014…68494504717641661279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.114 × 10¹¹⁸(119-digit number)
11142203072169205402…36989009435283322559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.228 × 10¹¹⁸(119-digit number)
22284406144338410805…73978018870566645119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
4.456 × 10¹¹⁸(119-digit number)
44568812288676821611…47956037741133290239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
8.913 × 10¹¹⁸(119-digit number)
89137624577353643223…95912075482266580479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.782 × 10¹¹⁹(120-digit number)
17827524915470728644…91824150964533160959
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:57,862,861 XPM·at block #6,827,343 · updates every 60s
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