Block #2,160,593

1CCLength 11★★★☆☆

Cunningham Chain of the First Kind · Discovered 6/14/2017, 5:17:16 PM · Difficulty 10.9012 · 4,656,191 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
c8d325b69f90b533ffd0c636c18746aa0a74abb54810145858c9c9cbf7ff8008

Height

#2,160,593

Difficulty

10.901249

Transactions

11

Size

4.38 KB

Version

2

Bits

0ae6b845

Nonce

379,575,799

Timestamp

6/14/2017, 5:17:16 PM

Confirmations

4,656,191

Merkle Root

130ae9ef61335f358e82e5e7b01dafbff015e27456aae28c2173bfb897f74e43
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.

5.313 × 10⁹³(94-digit number)
53130012892235637663…13226270349633293839
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
5.313 × 10⁹³(94-digit number)
53130012892235637663…13226270349633293839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.062 × 10⁹⁴(95-digit number)
10626002578447127532…26452540699266587679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
2.125 × 10⁹⁴(95-digit number)
21252005156894255065…52905081398533175359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
4.250 × 10⁹⁴(95-digit number)
42504010313788510131…05810162797066350719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
8.500 × 10⁹⁴(95-digit number)
85008020627577020262…11620325594132701439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.700 × 10⁹⁵(96-digit number)
17001604125515404052…23240651188265402879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.400 × 10⁹⁵(96-digit number)
34003208251030808104…46481302376530805759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.800 × 10⁹⁵(96-digit number)
68006416502061616209…92962604753061611519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.360 × 10⁹⁶(97-digit number)
13601283300412323241…85925209506123223039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.720 × 10⁹⁶(97-digit number)
27202566600824646483…71850419012246446079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
11
2^10 × origin − 1
5.440 × 10⁹⁶(97-digit number)
54405133201649292967…43700838024492892159
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:57,778,307 XPM·at block #6,816,783 · updates every 60s
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