Block #1,565,372

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/30/2016, 5:04:30 AM · Difficulty 10.7529 · 5,259,928 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
8e16413744bf0bdb5c13d369942fa302bac22a08acf28e5379f10684186f4596

Height

#1,565,372

Difficulty

10.752933

Transactions

2

Size

1.18 KB

Version

2

Bits

0ac0c03a

Nonce

578,646,640

Timestamp

4/30/2016, 5:04:30 AM

Confirmations

5,259,928

Merkle Root

5df3723f614e4ae13bfbfd65dbf82eef65966c4f7fc218f7ac62b2f2cb3b56bf
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.

1.095 × 10⁹³(94-digit number)
10950620866730956783…26465424351534416001
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
1.095 × 10⁹³(94-digit number)
10950620866730956783…26465424351534416001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.190 × 10⁹³(94-digit number)
21901241733461913566…52930848703068832001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.380 × 10⁹³(94-digit number)
43802483466923827132…05861697406137664001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.760 × 10⁹³(94-digit number)
87604966933847654265…11723394812275328001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.752 × 10⁹⁴(95-digit number)
17520993386769530853…23446789624550656001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.504 × 10⁹⁴(95-digit number)
35041986773539061706…46893579249101312001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.008 × 10⁹⁴(95-digit number)
70083973547078123412…93787158498202624001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.401 × 10⁹⁵(96-digit number)
14016794709415624682…87574316996405248001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.803 × 10⁹⁵(96-digit number)
28033589418831249364…75148633992810496001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.606 × 10⁹⁵(96-digit number)
56067178837662498729…50297267985620992001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.121 × 10⁹⁶(97-digit number)
11213435767532499745…00594535971241984001
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 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
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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,846,501 XPM·at block #6,825,299 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy