Block #383,200

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/31/2014, 6:45:21 AM · Difficulty 10.3910 · 6,443,852 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
918e5c5beae8607a4fcb3bc132986001879b2ec6c15b9d2dd89b7438d909de73

Height

#383,200

Difficulty

10.390998

Transactions

1

Size

869 B

Version

2

Bits

0a64186e

Nonce

4,914

Timestamp

1/31/2014, 6:45:21 AM

Confirmations

6,443,852

Merkle Root

d8d3ca3156abf456898906ec4b0a32d4f0bb9aefaa6d0ca3abf94737e25d0599
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.

1.104 × 10⁹⁹(100-digit number)
11049417931652108794…37091388876999934721
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
1.104 × 10⁹⁹(100-digit number)
11049417931652108794…37091388876999934721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.209 × 10⁹⁹(100-digit number)
22098835863304217589…74182777753999869441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.419 × 10⁹⁹(100-digit number)
44197671726608435179…48365555507999738881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.839 × 10⁹⁹(100-digit number)
88395343453216870359…96731111015999477761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.767 × 10¹⁰⁰(101-digit number)
17679068690643374071…93462222031998955521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.535 × 10¹⁰⁰(101-digit number)
35358137381286748143…86924444063997911041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.071 × 10¹⁰⁰(101-digit number)
70716274762573496287…73848888127995822081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.414 × 10¹⁰¹(102-digit number)
14143254952514699257…47697776255991644161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.828 × 10¹⁰¹(102-digit number)
28286509905029398515…95395552511983288321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.657 × 10¹⁰¹(102-digit number)
56573019810058797030…90791105023966576641
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:57,860,598 XPM·at block #6,827,051 · updates every 60s
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