Block #1,263,292

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 10/2/2015, 12:58:56 AM · Difficulty 10.8252 · 5,540,186 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
aa4403497409d1360cfa15f7d5da5cc81447179beda4fae2150178b22efb5e20

Height

#1,263,292

Difficulty

10.825178

Transactions

3

Size

650 B

Version

2

Bits

0ad33ee1

Nonce

778,031,678

Timestamp

10/2/2015, 12:58:56 AM

Confirmations

5,540,186

Merkle Root

a32688879e5a2bc79d0323854209d5a302abb31dc092c4e5d26d5e358d36c07b
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.

9.208 × 10⁹⁶(97-digit number)
92089098508307691880…74180927365454243839
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
9.208 × 10⁹⁶(97-digit number)
92089098508307691880…74180927365454243839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.841 × 10⁹⁷(98-digit number)
18417819701661538376…48361854730908487679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.683 × 10⁹⁷(98-digit number)
36835639403323076752…96723709461816975359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.367 × 10⁹⁷(98-digit number)
73671278806646153504…93447418923633950719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.473 × 10⁹⁸(99-digit number)
14734255761329230700…86894837847267901439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.946 × 10⁹⁸(99-digit number)
29468511522658461401…73789675694535802879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.893 × 10⁹⁸(99-digit number)
58937023045316922803…47579351389071605759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.178 × 10⁹⁹(100-digit number)
11787404609063384560…95158702778143211519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.357 × 10⁹⁹(100-digit number)
23574809218126769121…90317405556286423039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.714 × 10⁹⁹(100-digit number)
47149618436253538242…80634811112572846079
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:57,671,853 XPM·at block #6,803,477 · updates every 60s
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