Block #366,225

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 1/19/2014, 7:05:00 AM · Difficulty 10.4265 · 6,429,678 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
9b322fd4edb9cf0b80e3a05d33186387ec0c7deb6f11f33f0402da6a2c9db6e6

Height

#366,225

Difficulty

10.426506

Transactions

1

Size

229 B

Version

2

Bits

0a6d2f7a

Nonce

21,628

Timestamp

1/19/2014, 7:05:00 AM

Confirmations

6,429,678

Merkle Root

af396b81118a8304977c2593c6ac7bfff1a5a16afa1cb59637dadc9dc18c4531
Transactions (1)
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.

6.959 × 10¹⁰²(103-digit number)
69596568913314484472…51426078948305756161
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
6.959 × 10¹⁰²(103-digit number)
69596568913314484472…51426078948305756161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.391 × 10¹⁰³(104-digit number)
13919313782662896894…02852157896611512321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.783 × 10¹⁰³(104-digit number)
27838627565325793788…05704315793223024641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.567 × 10¹⁰³(104-digit number)
55677255130651587577…11408631586446049281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.113 × 10¹⁰⁴(105-digit number)
11135451026130317515…22817263172892098561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.227 × 10¹⁰⁴(105-digit number)
22270902052260635031…45634526345784197121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.454 × 10¹⁰⁴(105-digit number)
44541804104521270062…91269052691568394241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.908 × 10¹⁰⁴(105-digit number)
89083608209042540124…82538105383136788481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.781 × 10¹⁰⁵(106-digit number)
17816721641808508024…65076210766273576961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.563 × 10¹⁰⁵(106-digit number)
35633443283617016049…30152421532547153921
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:57,611,308 XPM·at block #6,795,902 · updates every 60s
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