Block #946,233

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 2/21/2015, 4:35:03 PM · Difficulty 10.8985 · 5,866,654 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
987a63692add6b6d69249a4a9b5b0495daa2f5915093615e89af4b59070ec218

Height

#946,233

Difficulty

10.898524

Transactions

4

Size

2.02 KB

Version

2

Bits

0ae605ad

Nonce

80,180,389

Timestamp

2/21/2015, 4:35:03 PM

Confirmations

5,866,654

Merkle Root

8ab918c81fadd4dacfa8da8c9c77614c62f3948e1d9e5dca40ae212c9ed7354f
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.

1.026 × 10⁹⁷(98-digit number)
10262306195543200537…70569140837004124161
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
1.026 × 10⁹⁷(98-digit number)
10262306195543200537…70569140837004124161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
2.052 × 10⁹⁷(98-digit number)
20524612391086401075…41138281674008248321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
4.104 × 10⁹⁷(98-digit number)
41049224782172802150…82276563348016496641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
8.209 × 10⁹⁷(98-digit number)
82098449564345604300…64553126696032993281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.641 × 10⁹⁸(99-digit number)
16419689912869120860…29106253392065986561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
3.283 × 10⁹⁸(99-digit number)
32839379825738241720…58212506784131973121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
6.567 × 10⁹⁸(99-digit number)
65678759651476483440…16425013568263946241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
1.313 × 10⁹⁹(100-digit number)
13135751930295296688…32850027136527892481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
2.627 × 10⁹⁹(100-digit number)
26271503860590593376…65700054273055784961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
5.254 × 10⁹⁹(100-digit number)
52543007721181186752…31400108546111569921
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:57,747,126 XPM·at block #6,812,886 · updates every 60s
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