Block #792,067

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 11/1/2014, 11:07:57 AM · Difficulty 10.9734 · 6,024,664 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
640dab98aa61623a9c048e11bb31aece6e2a31da2d5874e8e90f77882111e29e

Height

#792,067

Difficulty

10.973434

Transactions

3

Size

652 B

Version

2

Bits

0af932f8

Nonce

94,773,414

Timestamp

11/1/2014, 11:07:57 AM

Confirmations

6,024,664

Merkle Root

96ec4defcbe04ab0f8a7da1084158ede4fd6d556d1dd5cebc3ec77ea141eb9eb
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.

1.345 × 10⁹⁶(97-digit number)
13455195352730353982…51358460153586785279
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
1.345 × 10⁹⁶(97-digit number)
13455195352730353982…51358460153586785279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
2.691 × 10⁹⁶(97-digit number)
26910390705460707964…02716920307173570559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
5.382 × 10⁹⁶(97-digit number)
53820781410921415928…05433840614347141119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.076 × 10⁹⁷(98-digit number)
10764156282184283185…10867681228694282239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.152 × 10⁹⁷(98-digit number)
21528312564368566371…21735362457388564479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
4.305 × 10⁹⁷(98-digit number)
43056625128737132742…43470724914777128959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
8.611 × 10⁹⁷(98-digit number)
86113250257474265485…86941449829554257919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.722 × 10⁹⁸(99-digit number)
17222650051494853097…73882899659108515839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
3.444 × 10⁹⁸(99-digit number)
34445300102989706194…47765799318217031679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
6.889 × 10⁹⁸(99-digit number)
68890600205979412388…95531598636434063359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
1.377 × 10⁹⁹(100-digit number)
13778120041195882477…91063197272868126719
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,777,883 XPM·at block #6,816,730 · updates every 60s
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