Block #965,597

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 3/9/2015, 3:35:41 AM · Difficulty 10.8208 · 5,861,393 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
4ad4f35149ad65629a2c927616d549c5f5a76acb9e91a2f00bc30bbae5f08c14

Height

#965,597

Difficulty

10.820788

Transactions

4

Size

4.45 KB

Version

2

Bits

0ad21f2b

Nonce

184,821,616

Timestamp

3/9/2015, 3:35:41 AM

Confirmations

5,861,393

Merkle Root

0eadc58594583b8b13510be638ed05be79e08934c6ebc66786790868918905b0
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.

3.158 × 10⁹⁵(96-digit number)
31586725715046377411…28616169352641343041
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
3.158 × 10⁹⁵(96-digit number)
31586725715046377411…28616169352641343041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
6.317 × 10⁹⁵(96-digit number)
63173451430092754823…57232338705282686081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.263 × 10⁹⁶(97-digit number)
12634690286018550964…14464677410565372161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
2.526 × 10⁹⁶(97-digit number)
25269380572037101929…28929354821130744321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
5.053 × 10⁹⁶(97-digit number)
50538761144074203858…57858709642261488641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.010 × 10⁹⁷(98-digit number)
10107752228814840771…15717419284522977281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.021 × 10⁹⁷(98-digit number)
20215504457629681543…31434838569045954561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
4.043 × 10⁹⁷(98-digit number)
40431008915259363086…62869677138091909121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
8.086 × 10⁹⁷(98-digit number)
80862017830518726173…25739354276183818241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
1.617 × 10⁹⁸(99-digit number)
16172403566103745234…51478708552367636481
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:57,860,094 XPM·at block #6,826,989 · updates every 60s
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