Block #495,296

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 4/16/2014, 1:53:53 PM · Difficulty 10.7343 · 6,296,278 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
a8918ccb4c0ebac0afd9c7dfd2980d89e7abdcac53249c9564881f5554bf6c57

Height

#495,296

Difficulty

10.734307

Transactions

1

Size

833 B

Version

2

Bits

0abbfb91

Nonce

15,044

Timestamp

4/16/2014, 1:53:53 PM

Confirmations

6,296,278

Merkle Root

646c7d406b2f5319fbd87dd351d51ff3dd5c09664d7253c054572a40d3f8c5cd
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.

8.731 × 10⁹⁶(97-digit number)
87312356118697122499…13954385342770189441
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
8.731 × 10⁹⁶(97-digit number)
87312356118697122499…13954385342770189441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.746 × 10⁹⁷(98-digit number)
17462471223739424499…27908770685540378881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
3.492 × 10⁹⁷(98-digit number)
34924942447478848999…55817541371080757761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
6.984 × 10⁹⁷(98-digit number)
69849884894957697999…11635082742161515521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.396 × 10⁹⁸(99-digit number)
13969976978991539599…23270165484323031041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.793 × 10⁹⁸(99-digit number)
27939953957983079199…46540330968646062081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
5.587 × 10⁹⁸(99-digit number)
55879907915966158399…93080661937292124161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.117 × 10⁹⁹(100-digit number)
11175981583193231679…86161323874584248321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.235 × 10⁹⁹(100-digit number)
22351963166386463359…72322647749168496641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
4.470 × 10⁹⁹(100-digit number)
44703926332772926719…44645295498336993281
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:57,576,540 XPM·at block #6,791,573 · updates every 60s
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