Block #1,334,503

2CCLength 10★★☆☆☆

Cunningham Chain of the Second Kind · Discovered 11/20/2015, 8:01:47 AM · Difficulty 10.8354 · 5,476,565 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
f1f7315ee2f313183e086135f3e2d2d8a13ac55d740c34f889c246ef1659f6fb

Height

#1,334,503

Difficulty

10.835352

Transactions

2

Size

1.08 KB

Version

2

Bits

0ad5d99f

Nonce

618,027,822

Timestamp

11/20/2015, 8:01:47 AM

Confirmations

5,476,565

Merkle Root

569cee6d95f0d8d00ea56bdab5af56486fb0a10d78cf4c4488064511a0d66ed3
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.

6.435 × 10⁹⁶(97-digit number)
64357819041380952919…00791644121814794241
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
6.435 × 10⁹⁶(97-digit number)
64357819041380952919…00791644121814794241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
1.287 × 10⁹⁷(98-digit number)
12871563808276190583…01583288243629588481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
2.574 × 10⁹⁷(98-digit number)
25743127616552381167…03166576487259176961
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
5.148 × 10⁹⁷(98-digit number)
51486255233104762335…06333152974518353921
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
1.029 × 10⁹⁸(99-digit number)
10297251046620952467…12666305949036707841
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
2.059 × 10⁹⁸(99-digit number)
20594502093241904934…25332611898073415681
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
4.118 × 10⁹⁸(99-digit number)
41189004186483809868…50665223796146831361
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
8.237 × 10⁹⁸(99-digit number)
82378008372967619736…01330447592293662721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.647 × 10⁹⁹(100-digit number)
16475601674593523947…02660895184587325441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
3.295 × 10⁹⁹(100-digit number)
32951203349187047894…05321790369174650881
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:57,732,650 XPM·at block #6,811,067 · updates every 60s
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