Block #392,298

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/6/2014, 9:13:17 AM · Difficulty 10.4370 · 6,417,498 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4feec37fffc2f1d348fe3105fd78feae9b2e2c4aee53e289fb7221530f41b983

Height

#392,298

Difficulty

10.436966

Transactions

2

Size

689 B

Version

2

Bits

0a6fdd01

Nonce

291,706

Timestamp

2/6/2014, 9:13:17 AM

Confirmations

6,417,498

Merkle Root

a987ec97d5c8f40a68aaebab47b57992fd8dd98022870b3625482c6a9ff14fa2
Transactions (2)
1 in → 1 out9.1843 XPM110 B
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.

1.205 × 10¹⁰³(104-digit number)
12051619161410588694…40364568769009266561
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
1.205 × 10¹⁰³(104-digit number)
12051619161410588694…40364568769009266561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.410 × 10¹⁰³(104-digit number)
24103238322821177389…80729137538018533121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.820 × 10¹⁰³(104-digit number)
48206476645642354778…61458275076037066241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
9.641 × 10¹⁰³(104-digit number)
96412953291284709557…22916550152074132481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.928 × 10¹⁰⁴(105-digit number)
19282590658256941911…45833100304148264961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.856 × 10¹⁰⁴(105-digit number)
38565181316513883823…91666200608296529921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
7.713 × 10¹⁰⁴(105-digit number)
77130362633027767646…83332401216593059841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.542 × 10¹⁰⁵(106-digit number)
15426072526605553529…66664802433186119681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
3.085 × 10¹⁰⁵(106-digit number)
30852145053211107058…33329604866372239361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
6.170 × 10¹⁰⁵(106-digit number)
61704290106422214116…66659209732744478721
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:57,722,448 XPM·at block #6,809,795 · updates every 60s
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