Block #466,178

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/29/2014, 11:59:02 PM · Difficulty 10.4225 · 6,323,693 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
c7afc7129e9fa24188424df2f5e08e528f099b39e2854187829e1fae3527027c

Height

#466,178

Difficulty

10.422491

Transactions

2

Size

872 B

Version

2

Bits

0a6c2864

Nonce

63,749

Timestamp

3/29/2014, 11:59:02 PM

Confirmations

6,323,693

Merkle Root

bbc1caa2f6ddfb4cb3920525584d5a933c0101058fe1eb549d92445031264f1a
Transactions (2)
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.

5.652 × 10¹⁰²(103-digit number)
56525007524944368880…10642039679179364161
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
5.652 × 10¹⁰²(103-digit number)
56525007524944368880…10642039679179364161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.130 × 10¹⁰³(104-digit number)
11305001504988873776…21284079358358728321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.261 × 10¹⁰³(104-digit number)
22610003009977747552…42568158716717456641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
4.522 × 10¹⁰³(104-digit number)
45220006019955495104…85136317433434913281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
9.044 × 10¹⁰³(104-digit number)
90440012039910990208…70272634866869826561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.808 × 10¹⁰⁴(105-digit number)
18088002407982198041…40545269733739653121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
3.617 × 10¹⁰⁴(105-digit number)
36176004815964396083…81090539467479306241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
7.235 × 10¹⁰⁴(105-digit number)
72352009631928792166…62181078934958612481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.447 × 10¹⁰⁵(106-digit number)
14470401926385758433…24362157869917224961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.894 × 10¹⁰⁵(106-digit number)
28940803852771516866…48724315739834449921
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:57,562,941 XPM·at block #6,789,870 · updates every 60s