Block #23,994

1CCLength 7★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/12/2013, 9:41:13 PM · Difficulty 7.9631 · 6,800,754 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1fa4e02fc6195b8aaecdb6496ff19f232e8a873058f639f2e3dd5f9870085d24

Height

#23,994

Difficulty

7.963117

Transactions

2

Size

357 B

Version

2

Bits

07f68ed2

Nonce

633

Timestamp

7/12/2013, 9:41:13 PM

Confirmations

6,800,754

Merkle Root

d691892564973ce5c3762186ae2f54cf2f8ba9806490f4d0ca7e49f41acdfc79
Transactions (2)
1 in → 1 out15.7600 XPM108 B
1 in → 1 out16.0400 XPM158 B
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.

1.143 × 10⁹⁸(99-digit number)
11431471472106881679…41810994505712689719
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
1.143 × 10⁹⁸(99-digit number)
11431471472106881679…41810994505712689719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.286 × 10⁹⁸(99-digit number)
22862942944213763358…83621989011425379439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
4.572 × 10⁹⁸(99-digit number)
45725885888427526717…67243978022850758879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
9.145 × 10⁹⁸(99-digit number)
91451771776855053435…34487956045701517759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.829 × 10⁹⁹(100-digit number)
18290354355371010687…68975912091403035519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
3.658 × 10⁹⁹(100-digit number)
36580708710742021374…37951824182806071039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
7.316 × 10⁹⁹(100-digit number)
73161417421484042748…75903648365612142079
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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:57,842,055 XPM·at block #6,824,747 · updates every 60s
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