Block #784,250

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 10/26/2014, 6:13:46 PM · Difficulty 10.9751 · 6,006,694 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
34abab14692a5512a3549fd9ecb7b9821c51045ac93605e484c0d19a686da9d6

Height

#784,250

Difficulty

10.975145

Transactions

3

Size

13.46 KB

Version

2

Bits

0af9a321

Nonce

100,146,173

Timestamp

10/26/2014, 6:13:46 PM

Confirmations

6,006,694

Merkle Root

ea2f8dd6e7ea079fb419b71d399d5dbb801bcb2da4f66d006091d340a5e670e1
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.

7.866 × 10⁹⁴(95-digit number)
78661895654477122811…37729615957937321969
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
7.866 × 10⁹⁴(95-digit number)
78661895654477122811…37729615957937321969
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.573 × 10⁹⁵(96-digit number)
15732379130895424562…75459231915874643939
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.146 × 10⁹⁵(96-digit number)
31464758261790849124…50918463831749287879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.292 × 10⁹⁵(96-digit number)
62929516523581698249…01836927663498575759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.258 × 10⁹⁶(97-digit number)
12585903304716339649…03673855326997151519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.517 × 10⁹⁶(97-digit number)
25171806609432679299…07347710653994303039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.034 × 10⁹⁶(97-digit number)
50343613218865358599…14695421307988606079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.006 × 10⁹⁷(98-digit number)
10068722643773071719…29390842615977212159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.013 × 10⁹⁷(98-digit number)
20137445287546143439…58781685231954424319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.027 × 10⁹⁷(98-digit number)
40274890575092286879…17563370463908848639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
8.054 × 10⁹⁷(98-digit number)
80549781150184573758…35126740927817697279
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:57,571,554 XPM·at block #6,790,942 · updates every 60s