Block #1,100,988

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 6/12/2015, 6:24:58 AM · Difficulty 10.7599 · 5,716,502 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1cadd61578f6ab736b64969dc4f15013f9f95359d91ba1b04c071037cf5b3a4d

Height

#1,100,988

Difficulty

10.759921

Transactions

3

Size

17.97 KB

Version

2

Bits

0ac28a2b

Nonce

942,202,373

Timestamp

6/12/2015, 6:24:58 AM

Confirmations

5,716,502

Merkle Root

3081b050fc6ad94a3c55de6190fe259cfe18fa498eb4586677d38a9d7617d372
Transactions (3)
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.

4.700 × 10⁹⁵(96-digit number)
47004963660351029497…14124882905824823679
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
4.700 × 10⁹⁵(96-digit number)
47004963660351029497…14124882905824823679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
9.400 × 10⁹⁵(96-digit number)
94009927320702058994…28249765811649647359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
1.880 × 10⁹⁶(97-digit number)
18801985464140411798…56499531623299294719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
3.760 × 10⁹⁶(97-digit number)
37603970928280823597…12999063246598589439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
7.520 × 10⁹⁶(97-digit number)
75207941856561647195…25998126493197178879
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
1.504 × 10⁹⁷(98-digit number)
15041588371312329439…51996252986394357759
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
3.008 × 10⁹⁷(98-digit number)
30083176742624658878…03992505972788715519
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
6.016 × 10⁹⁷(98-digit number)
60166353485249317756…07985011945577431039
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
1.203 × 10⁹⁸(99-digit number)
12033270697049863551…15970023891154862079
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
2.406 × 10⁹⁸(99-digit number)
24066541394099727102…31940047782309724159
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:57,783,967 XPM·at block #6,817,489 · updates every 60s
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