Block #2,333,760

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/12/2017, 11:53:50 AM · Difficulty 10.9215 · 4,473,722 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
7f2556731f1f3ffc720a9eee00eb9a16ab1ca4d539faf273f8987dd96954e834

Height

#2,333,760

Difficulty

10.921462

Transactions

2

Size

755 B

Version

2

Bits

0aebe4f2

Nonce

991,246,713

Timestamp

10/12/2017, 11:53:50 AM

Confirmations

4,473,722

Merkle Root

0ee98cdb27228dea9092389910df14669ad2452b40971f43d83bda4c49d24ae5
Transactions (2)
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.

2.817 × 10⁹⁵(96-digit number)
28177611371377908828…90974943515252368801
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
2.817 × 10⁹⁵(96-digit number)
28177611371377908828…90974943515252368801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.635 × 10⁹⁵(96-digit number)
56355222742755817656…81949887030504737601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.127 × 10⁹⁶(97-digit number)
11271044548551163531…63899774061009475201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.254 × 10⁹⁶(97-digit number)
22542089097102327062…27799548122018950401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.508 × 10⁹⁶(97-digit number)
45084178194204654125…55599096244037900801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.016 × 10⁹⁶(97-digit number)
90168356388409308251…11198192488075801601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.803 × 10⁹⁷(98-digit number)
18033671277681861650…22396384976151603201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.606 × 10⁹⁷(98-digit number)
36067342555363723300…44792769952303206401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.213 × 10⁹⁷(98-digit number)
72134685110727446600…89585539904606412801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.442 × 10⁹⁸(99-digit number)
14426937022145489320…79171079809212825601
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:57,703,882 XPM·at block #6,807,481 · 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.

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