Block #1,106,514

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/15/2015, 10:45:03 AM · Difficulty 10.8011 · 5,699,953 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
d3449ca3d16f8e1a544b808ce0a3c25ca0f90fe2bc4963f29360c97e1405b15a

Height

#1,106,514

Difficulty

10.801108

Transactions

2

Size

1.14 KB

Version

2

Bits

0acd156d

Nonce

217,325,529

Timestamp

6/15/2015, 10:45:03 AM

Confirmations

5,699,953

Merkle Root

2cc0b2ce73e4096d67f378035dcfac6f22cf29582e262f466a56c1b5ee5729d3
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.

2.794 × 10⁹⁶(97-digit number)
27946149534603219610…09927228407905233919
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
2.794 × 10⁹⁶(97-digit number)
27946149534603219610…09927228407905233919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
5.589 × 10⁹⁶(97-digit number)
55892299069206439221…19854456815810467839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.117 × 10⁹⁷(98-digit number)
11178459813841287844…39708913631620935679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
2.235 × 10⁹⁷(98-digit number)
22356919627682575688…79417827263241871359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
4.471 × 10⁹⁷(98-digit number)
44713839255365151377…58835654526483742719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
8.942 × 10⁹⁷(98-digit number)
89427678510730302754…17671309052967485439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.788 × 10⁹⁸(99-digit number)
17885535702146060550…35342618105934970879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.577 × 10⁹⁸(99-digit number)
35771071404292121101…70685236211869941759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
7.154 × 10⁹⁸(99-digit number)
71542142808584242203…41370472423739883519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.430 × 10⁹⁹(100-digit number)
14308428561716848440…82740944847479767039
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:57,695,829 XPM·at block #6,806,466 · updates every 60s
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