Block #2,093,800

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2017, 4:39:12 AM · Difficulty 10.8712 · 4,737,538 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
0eda691a85bcc60d9a07647f6ddc3a978c1273291984ce18ab273dbfd5d75a5c

Height

#2,093,800

Difficulty

10.871205

Transactions

2

Size

2.11 KB

Version

2

Bits

0adf0748

Nonce

1,704,898,060

Timestamp

4/30/2017, 4:39:12 AM

Confirmations

4,737,538

Merkle Root

418672ac3e1582bee7d9445e3106d2da056cbb8b78cb311759f94ef41f50f9fa
Transactions (2)
1 in → 1 out8.4800 XPM109 B
13 in → 1 out65.9031 XPM1.92 KB
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.

2.266 × 10⁹⁴(95-digit number)
22661898450098953547…61212825312160086001
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
2.266 × 10⁹⁴(95-digit number)
22661898450098953547…61212825312160086001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.532 × 10⁹⁴(95-digit number)
45323796900197907094…22425650624320172001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.064 × 10⁹⁴(95-digit number)
90647593800395814188…44851301248640344001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.812 × 10⁹⁵(96-digit number)
18129518760079162837…89702602497280688001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.625 × 10⁹⁵(96-digit number)
36259037520158325675…79405204994561376001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.251 × 10⁹⁵(96-digit number)
72518075040316651350…58810409989122752001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.450 × 10⁹⁶(97-digit number)
14503615008063330270…17620819978245504001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.900 × 10⁹⁶(97-digit number)
29007230016126660540…35241639956491008001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
5.801 × 10⁹⁶(97-digit number)
58014460032253321080…70483279912982016001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.160 × 10⁹⁷(98-digit number)
11602892006450664216…40966559825964032001
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 Second 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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,894,857 XPM·at block #6,831,337 · updates every 60s
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