Block #180,600

2CCLength 9★☆☆☆☆

Cunningham Chain of the Second Kind · Discovered 9/25/2013, 10:32:45 PM · Difficulty 9.8621 · 6,644,531 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
83ba618f9022887e16ecb08124b96509bb2c271300f42eca006b055982ae7e40

Height

#180,600

Difficulty

9.862071

Transactions

3

Size

796 B

Version

2

Bits

09dcb0b1

Nonce

148,722

Timestamp

9/25/2013, 10:32:45 PM

Confirmations

6,644,531

Merkle Root

8289d07fdca60ed6cd1b5006a597c06f4c7e492d73ece43866818719c120abf0
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.

2.345 × 10⁹³(94-digit number)
23456838846971332526…37368069937577745351
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
2.345 × 10⁹³(94-digit number)
23456838846971332526…37368069937577745351
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
4.691 × 10⁹³(94-digit number)
46913677693942665052…74736139875155490701
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
9.382 × 10⁹³(94-digit number)
93827355387885330104…49472279750310981401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.876 × 10⁹⁴(95-digit number)
18765471077577066020…98944559500621962801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
3.753 × 10⁹⁴(95-digit number)
37530942155154132041…97889119001243925601
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
7.506 × 10⁹⁴(95-digit number)
75061884310308264083…95778238002487851201
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.501 × 10⁹⁵(96-digit number)
15012376862061652816…91556476004975702401
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
3.002 × 10⁹⁵(96-digit number)
30024753724123305633…83112952009951404801
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
6.004 × 10⁹⁵(96-digit number)
60049507448246611266…66225904019902809601
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,845,132 XPM·at block #6,825,130 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.
Privacy Policy·

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy