Block #696,760

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 8/28/2014, 11:35:53 AM · Difficulty 10.9582 · 6,110,320 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
8769dae1d1a2151f64aa8ceaff96c6ef17858ee97546392b09fb07d258190777

Height

#696,760

Difficulty

10.958247

Transactions

3

Size

659 B

Version

2

Bits

0af54fa5

Nonce

2,791,076,661

Timestamp

8/28/2014, 11:35:53 AM

Confirmations

6,110,320

Merkle Root

d8a67bafa1ec6edbb029c01a8f7f0a035609959905be054fdde25ad317e50d2d
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.

8.993 × 10⁹⁶(97-digit number)
89935098877651856484…75385929473794908159
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
8.993 × 10⁹⁶(97-digit number)
89935098877651856484…75385929473794908159
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
1.798 × 10⁹⁷(98-digit number)
17987019775530371296…50771858947589816319
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
3.597 × 10⁹⁷(98-digit number)
35974039551060742593…01543717895179632639
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
7.194 × 10⁹⁷(98-digit number)
71948079102121485187…03087435790359265279
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
1.438 × 10⁹⁸(99-digit number)
14389615820424297037…06174871580718530559
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
2.877 × 10⁹⁸(99-digit number)
28779231640848594075…12349743161437061119
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
5.755 × 10⁹⁸(99-digit number)
57558463281697188150…24699486322874122239
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
1.151 × 10⁹⁹(100-digit number)
11511692656339437630…49398972645748244479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
2.302 × 10⁹⁹(100-digit number)
23023385312678875260…98797945291496488959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
4.604 × 10⁹⁹(100-digit number)
46046770625357750520…97595890582992977919
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:57,700,736 XPM·at block #6,807,079 · updates every 60s
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