Block #1,226,800

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/8/2015, 3:08:31 AM · Difficulty 10.7353 · 5,563,118 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
36d682d500c0c81186d662260c7b27315374a2839822180c182a009fd753e7b6

Height

#1,226,800

Difficulty

10.735335

Transactions

4

Size

1.01 KB

Version

2

Bits

0abc3eef

Nonce

876,548,688

Timestamp

9/8/2015, 3:08:31 AM

Confirmations

5,563,118

Merkle Root

b2caad54842068b8e49f7897cc4234d69046f80adf367872b6a1536bc06fc4b1
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.

2.827 × 10⁹⁶(97-digit number)
28276661087592785902…99662177340774888961
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
2.827 × 10⁹⁶(97-digit number)
28276661087592785902…99662177340774888961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
5.655 × 10⁹⁶(97-digit number)
56553322175185571804…99324354681549777921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.131 × 10⁹⁷(98-digit number)
11310664435037114360…98648709363099555841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.262 × 10⁹⁷(98-digit number)
22621328870074228721…97297418726199111681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
4.524 × 10⁹⁷(98-digit number)
45242657740148457443…94594837452398223361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
9.048 × 10⁹⁷(98-digit number)
90485315480296914887…89189674904796446721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.809 × 10⁹⁸(99-digit number)
18097063096059382977…78379349809592893441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.619 × 10⁹⁸(99-digit number)
36194126192118765954…56758699619185786881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
7.238 × 10⁹⁸(99-digit number)
72388252384237531909…13517399238371573761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.447 × 10⁹⁹(100-digit number)
14477650476847506381…27034798476743147521
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:57,563,323 XPM·at block #6,789,917 · updates every 60s