Block #1,967,852

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/3/2017, 9:56:44 PM · Difficulty 10.7524 · 4,850,022 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
94444ac9e984ca8d4c1f9cad9d3b783d0a56c2f4373dc82e2210cb286331209c

Height

#1,967,852

Difficulty

10.752409

Transactions

2

Size

3.00 KB

Version

2

Bits

0ac09ddd

Nonce

757,413,386

Timestamp

2/3/2017, 9:56:44 PM

Confirmations

4,850,022

Merkle Root

cf96f3deb046f6be6ec973ed5d099894e1c15deee4ea3a262aa85ac5bd9e971b
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.

6.768 × 10⁹⁵(96-digit number)
67689362457182789469…05331368268210304001
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
6.768 × 10⁹⁵(96-digit number)
67689362457182789469…05331368268210304001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.353 × 10⁹⁶(97-digit number)
13537872491436557893…10662736536420608001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.707 × 10⁹⁶(97-digit number)
27075744982873115787…21325473072841216001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.415 × 10⁹⁶(97-digit number)
54151489965746231575…42650946145682432001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.083 × 10⁹⁷(98-digit number)
10830297993149246315…85301892291364864001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.166 × 10⁹⁷(98-digit number)
21660595986298492630…70603784582729728001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.332 × 10⁹⁷(98-digit number)
43321191972596985260…41207569165459456001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.664 × 10⁹⁷(98-digit number)
86642383945193970520…82415138330918912001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.732 × 10⁹⁸(99-digit number)
17328476789038794104…64830276661837824001
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.465 × 10⁹⁸(99-digit number)
34656953578077588208…29660553323675648001
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:57,787,051 XPM·at block #6,817,873 · updates every 60s
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