Block #2,466,800

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 1/10/2018, 3:09:18 PM · Difficulty 10.9607 · 4,375,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9a57967c53a4e5839792814b9b5153e029c7fae4391948d48128e3c37cf6dbec

Height

#2,466,800

Difficulty

10.960730

Transactions

5

Size

1.62 KB

Version

2

Bits

0af5f26d

Nonce

499,615,211

Timestamp

1/10/2018, 3:09:18 PM

Confirmations

4,375,445

Merkle Root

ba4fb467f7a930d855119eb5598c65d4d464b8e6d44b7f5154179840d9b838b6
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.

7.209 × 10⁹⁵(96-digit number)
72090088320382233929…48210351947414822401
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
7.209 × 10⁹⁵(96-digit number)
72090088320382233929…48210351947414822401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.441 × 10⁹⁶(97-digit number)
14418017664076446785…96420703894829644801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.883 × 10⁹⁶(97-digit number)
28836035328152893571…92841407789659289601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.767 × 10⁹⁶(97-digit number)
57672070656305787143…85682815579318579201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.153 × 10⁹⁷(98-digit number)
11534414131261157428…71365631158637158401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.306 × 10⁹⁷(98-digit number)
23068828262522314857…42731262317274316801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.613 × 10⁹⁷(98-digit number)
46137656525044629714…85462524634548633601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
9.227 × 10⁹⁷(98-digit number)
92275313050089259429…70925049269097267201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.845 × 10⁹⁸(99-digit number)
18455062610017851885…41850098538194534401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.691 × 10⁹⁸(99-digit number)
36910125220035703771…83700197076389068801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
7.382 × 10⁹⁸(99-digit number)
73820250440071407543…67400394152778137601
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:57,982,358 XPM·at block #6,842,244 · 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