Block #1,294,320

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 10/22/2015, 7:03:20 PM · Difficulty 10.8615 · 5,498,193 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
fa9c6c9528ee2d49a118be4d74c37238014cb8284bf2c40d1e64b12fa354fcea

Height

#1,294,320

Difficulty

10.861472

Transactions

3

Size

652 B

Version

2

Bits

0adc8973

Nonce

700,748,937

Timestamp

10/22/2015, 7:03:20 PM

Confirmations

5,498,193

Merkle Root

379b4a9a256db643f31f3ba49aab125059848a7793f7b11fe14ce56aabbf68e3
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.

4.045 × 10⁹⁴(95-digit number)
40456028031755803303…45400271016986746881
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
4.045 × 10⁹⁴(95-digit number)
40456028031755803303…45400271016986746881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
8.091 × 10⁹⁴(95-digit number)
80912056063511606607…90800542033973493761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.618 × 10⁹⁵(96-digit number)
16182411212702321321…81601084067946987521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.236 × 10⁹⁵(96-digit number)
32364822425404642642…63202168135893975041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.472 × 10⁹⁵(96-digit number)
64729644850809285285…26404336271787950081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.294 × 10⁹⁶(97-digit number)
12945928970161857057…52808672543575900161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.589 × 10⁹⁶(97-digit number)
25891857940323714114…05617345087151800321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.178 × 10⁹⁶(97-digit number)
51783715880647428228…11234690174303600641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.035 × 10⁹⁷(98-digit number)
10356743176129485645…22469380348607201281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.071 × 10⁹⁷(98-digit number)
20713486352258971291…44938760697214402561
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:57,584,070 XPM·at block #6,792,512 · updates every 60s
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