Block #1,453,565

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/12/2016, 8:45:48 PM · Difficulty 10.7271 · 5,386,870 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
7111e592706092a53c9c4fe2198e102e2f4acd54f4db8ee92359936bbf67583e

Height

#1,453,565

Difficulty

10.727069

Transactions

2

Size

2.87 KB

Version

2

Bits

0aba2137

Nonce

609,782,952

Timestamp

2/12/2016, 8:45:48 PM

Confirmations

5,386,870

Merkle Root

201ff6f85776060db0f86afafa32dcb7a2a930707e21c52766e3b9a6c7c70ca2
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.

2.216 × 10⁹⁵(96-digit number)
22164601110703841352…08404926071598079039
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
2.216 × 10⁹⁵(96-digit number)
22164601110703841352…08404926071598079039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.432 × 10⁹⁵(96-digit number)
44329202221407682705…16809852143196158079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.865 × 10⁹⁵(96-digit number)
88658404442815365411…33619704286392316159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.773 × 10⁹⁶(97-digit number)
17731680888563073082…67239408572784632319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.546 × 10⁹⁶(97-digit number)
35463361777126146164…34478817145569264639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.092 × 10⁹⁶(97-digit number)
70926723554252292329…68957634291138529279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.418 × 10⁹⁷(98-digit number)
14185344710850458465…37915268582277058559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.837 × 10⁹⁷(98-digit number)
28370689421700916931…75830537164554117119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.674 × 10⁹⁷(98-digit number)
56741378843401833863…51661074329108234239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.134 × 10⁹⁸(99-digit number)
11348275768680366772…03322148658216468479
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:57,967,807 XPM·at block #6,840,434 · updates every 60s
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