Block #1,337,605

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2015, 4:34:54 AM · Difficulty 10.7990 · 5,458,967 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
f44ec8a20eec8d793d085880f98198e97043150b2fa46f32cc9847d57f25dae0

Height

#1,337,605

Difficulty

10.798972

Transactions

2

Size

1.28 KB

Version

2

Bits

0acc8966

Nonce

795,999,856

Timestamp

11/23/2015, 4:34:54 AM

Confirmations

5,458,967

Merkle Root

4bca3b159863d21b6637f41f1363455cc2120710f09e447928a767ace1f53b70
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.

8.669 × 10⁹⁵(96-digit number)
86693579633754403215…57874066717198815999
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
8.669 × 10⁹⁵(96-digit number)
86693579633754403215…57874066717198815999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.733 × 10⁹⁶(97-digit number)
17338715926750880643…15748133434397631999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.467 × 10⁹⁶(97-digit number)
34677431853501761286…31496266868795263999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
6.935 × 10⁹⁶(97-digit number)
69354863707003522572…62992533737590527999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.387 × 10⁹⁷(98-digit number)
13870972741400704514…25985067475181055999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.774 × 10⁹⁷(98-digit number)
27741945482801409029…51970134950362111999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.548 × 10⁹⁷(98-digit number)
55483890965602818058…03940269900724223999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.109 × 10⁹⁸(99-digit number)
11096778193120563611…07880539801448447999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.219 × 10⁹⁸(99-digit number)
22193556386241127223…15761079602896895999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.438 × 10⁹⁸(99-digit number)
44387112772482254446…31522159205793791999
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 First 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 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,616,577 XPM·at block #6,796,571 · updates every 60s
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