Block #59,860

1CCLength 8★☆☆☆☆

Cunningham Chain of the First Kind · Discovered 7/18/2013, 4:44:27 AM · Difficulty 8.9668 · 6,730,199 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
1b1fbcbd28ae90697aa1a2f5efe240dd32cfb411fb1d39713f5b81b3d1181c90

Height

#59,860

Difficulty

8.966762

Transactions

5

Size

1.41 KB

Version

2

Bits

08f77db1

Nonce

121

Timestamp

7/18/2013, 4:44:27 AM

Confirmations

6,730,199

Merkle Root

86314477aa1db0b51bbc22cdf33b753c72b46359c4ac78a27387f044dfe4c1ce
Transactions (5)
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.

1.580 × 10⁹⁸(99-digit number)
15803928088993711222…85447490153990608099
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
1.580 × 10⁹⁸(99-digit number)
15803928088993711222…85447490153990608099
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
3.160 × 10⁹⁸(99-digit number)
31607856177987422444…70894980307981216199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
6.321 × 10⁹⁸(99-digit number)
63215712355974844888…41789960615962432399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.264 × 10⁹⁹(100-digit number)
12643142471194968977…83579921231924864799
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
2.528 × 10⁹⁹(100-digit number)
25286284942389937955…67159842463849729599
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
5.057 × 10⁹⁹(100-digit number)
50572569884779875910…34319684927699459199
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.011 × 10¹⁰⁰(101-digit number)
10114513976955975182…68639369855398918399
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.022 × 10¹⁰⁰(101-digit number)
20229027953911950364…37278739710797836799
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 8 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
CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,564,445 XPM·at block #6,790,058 · updates every 60s