Block #2,284,506

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 9/6/2017, 6:13:24 AM · Difficulty 10.9550 · 4,546,389 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8e11cd028c867bcc8abe23c923732df452666d63fdb537b38cb0e6c052237ae

Height

#2,284,506

Difficulty

10.955025

Transactions

4

Size

1.87 KB

Version

2

Bits

0af47c7d

Nonce

110,943,828

Timestamp

9/6/2017, 6:13:24 AM

Confirmations

4,546,389

Merkle Root

e6d9c25cb38eaa5fbfc5d5fd917826d02883966de1a67794d08a4ec32881a990
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.

8.413 × 10⁹⁴(95-digit number)
84137581420995384539…87044481912695984481
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
8.413 × 10⁹⁴(95-digit number)
84137581420995384539…87044481912695984481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.682 × 10⁹⁵(96-digit number)
16827516284199076907…74088963825391968961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.365 × 10⁹⁵(96-digit number)
33655032568398153815…48177927650783937921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.731 × 10⁹⁵(96-digit number)
67310065136796307631…96355855301567875841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.346 × 10⁹⁶(97-digit number)
13462013027359261526…92711710603135751681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.692 × 10⁹⁶(97-digit number)
26924026054718523052…85423421206271503361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.384 × 10⁹⁶(97-digit number)
53848052109437046105…70846842412543006721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.076 × 10⁹⁷(98-digit number)
10769610421887409221…41693684825086013441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.153 × 10⁹⁷(98-digit number)
21539220843774818442…83387369650172026881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.307 × 10⁹⁷(98-digit number)
43078441687549636884…66774739300344053761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
8.615 × 10⁹⁷(98-digit number)
86156883375099273768…33549478600688107521
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:57,891,287 XPM·at block #6,830,894 · updates every 60s
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