Block #1,775,850

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/23/2016, 8:53:06 AM · Difficulty 10.7599 · 5,038,618 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
26dfb280ae8b8ab0faade2d3f6cd6c7fd52da699defc7dc43851c6480f47c42b

Height

#1,775,850

Difficulty

10.759927

Transactions

2

Size

426 B

Version

2

Bits

0ac28a90

Nonce

1,023,405,463

Timestamp

9/23/2016, 8:53:06 AM

Confirmations

5,038,618

Merkle Root

df9c31ad05334f7e559c2e43c5094e009c47707b7dec1f07632618bd17c90610
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.

1.327 × 10⁹⁷(98-digit number)
13275848617233315139…95682063292986903041
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
1.327 × 10⁹⁷(98-digit number)
13275848617233315139…95682063292986903041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.655 × 10⁹⁷(98-digit number)
26551697234466630279…91364126585973806081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
5.310 × 10⁹⁷(98-digit number)
53103394468933260559…82728253171947612161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.062 × 10⁹⁸(99-digit number)
10620678893786652111…65456506343895224321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.124 × 10⁹⁸(99-digit number)
21241357787573304223…30913012687790448641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
4.248 × 10⁹⁸(99-digit number)
42482715575146608447…61826025375580897281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
8.496 × 10⁹⁸(99-digit number)
84965431150293216895…23652050751161794561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.699 × 10⁹⁹(100-digit number)
16993086230058643379…47304101502323589121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.398 × 10⁹⁹(100-digit number)
33986172460117286758…94608203004647178241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.797 × 10⁹⁹(100-digit number)
67972344920234573516…89216406009294356481
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:57,759,817 XPM·at block #6,814,467 · updates every 60s
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