Block #1,464,812

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/19/2016, 10:26:36 PM · Difficulty 10.7795 · 5,378,445 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
12a5ca879ac2aa9cdfca1ba23d936e46318ab863938d4b4376a473e7d8c41e5d

Height

#1,464,812

Difficulty

10.779453

Transactions

2

Size

1.14 KB

Version

2

Bits

0ac78a3a

Nonce

329,669,614

Timestamp

2/19/2016, 10:26:36 PM

Confirmations

5,378,445

Merkle Root

4d57b0ecbdc9ab2ae4aed952e7cc13e05844cebacaf03696f99cf1d2ec9e3d93
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.

3.572 × 10⁹⁵(96-digit number)
35724284629448658184…49400777315821962881
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
3.572 × 10⁹⁵(96-digit number)
35724284629448658184…49400777315821962881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.144 × 10⁹⁵(96-digit number)
71448569258897316368…98801554631643925761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.428 × 10⁹⁶(97-digit number)
14289713851779463273…97603109263287851521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.857 × 10⁹⁶(97-digit number)
28579427703558926547…95206218526575703041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.715 × 10⁹⁶(97-digit number)
57158855407117853095…90412437053151406081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.143 × 10⁹⁷(98-digit number)
11431771081423570619…80824874106302812161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.286 × 10⁹⁷(98-digit number)
22863542162847141238…61649748212605624321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.572 × 10⁹⁷(98-digit number)
45727084325694282476…23299496425211248641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
9.145 × 10⁹⁷(98-digit number)
91454168651388564952…46598992850422497281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.829 × 10⁹⁸(99-digit number)
18290833730277712990…93197985700844994561
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:57,990,428 XPM·at block #6,843,256 · updates every 60s
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