Block #1,337,817

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 11/23/2015, 9:05:15 AM · Difficulty 10.7967 · 5,467,409 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
e290a2c8bfc5a5b0dce810060e93f82f212a1feff0db8dfd5d685e7205b12ca4

Height

#1,337,817

Difficulty

10.796652

Transactions

2

Size

1.18 KB

Version

2

Bits

0acbf166

Nonce

1,519,812,395

Timestamp

11/23/2015, 9:05:15 AM

Confirmations

5,467,409

Merkle Root

79ca523c4ad93fd393ad5bd6398b9dbdd4c3a57031b4546055b0771bbdba06a1
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.

2.700 × 10⁹⁴(95-digit number)
27004225147448631043…10174365953026170159
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
2.700 × 10⁹⁴(95-digit number)
27004225147448631043…10174365953026170159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.400 × 10⁹⁴(95-digit number)
54008450294897262087…20348731906052340319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.080 × 10⁹⁵(96-digit number)
10801690058979452417…40697463812104680639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.160 × 10⁹⁵(96-digit number)
21603380117958904835…81394927624209361279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.320 × 10⁹⁵(96-digit number)
43206760235917809670…62789855248418722559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.641 × 10⁹⁵(96-digit number)
86413520471835619340…25579710496837445119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.728 × 10⁹⁶(97-digit number)
17282704094367123868…51159420993674890239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.456 × 10⁹⁶(97-digit number)
34565408188734247736…02318841987349780479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.913 × 10⁹⁶(97-digit number)
69130816377468495472…04637683974699560959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.382 × 10⁹⁷(98-digit number)
13826163275493699094…09275367949399121919
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:57,685,882 XPM·at block #6,805,225 · updates every 60s
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