1. #6,817,6281CC10 primes

    Cunningham 1st · ⛏️ coinsforall.io

Block #1,023,555

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 4/19/2015, 12:55:22 PM · Difficulty 10.7543 · 5,794,074 confirmations

1CC
Cunningham Chain of the First Kind

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

Block Header
Block Hash
ebed785d89d8717107aabd7dddc3b815b1144e05473a59d74bc913d9604fb262

Height

#1,023,555

Difficulty

10.754289

Transactions

3

Size

945 B

Version

2

Bits

0ac1190e

Nonce

207,704,146

Timestamp

4/19/2015, 12:55:22 PM

Confirmations

5,794,074

Merkle Root

c4e7f8ee7847a6131c5cec1a4aa9b1a8ff3b4cfa327b17f18f3049431deaf5de
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.

2.208 × 10⁹⁴(95-digit number)
22080017205150905408…16786005864516194739
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
2.208 × 10⁹⁴(95-digit number)
22080017205150905408…16786005864516194739
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.416 × 10⁹⁴(95-digit number)
44160034410301810817…33572011729032389479
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
8.832 × 10⁹⁴(95-digit number)
88320068820603621634…67144023458064778959
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.766 × 10⁹⁵(96-digit number)
17664013764120724326…34288046916129557919
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.532 × 10⁹⁵(96-digit number)
35328027528241448653…68576093832259115839
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.065 × 10⁹⁵(96-digit number)
70656055056482897307…37152187664518231679
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.413 × 10⁹⁶(97-digit number)
14131211011296579461…74304375329036463359
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
2.826 × 10⁹⁶(97-digit number)
28262422022593158922…48608750658072926719
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
5.652 × 10⁹⁶(97-digit number)
56524844045186317845…97217501316145853439
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.130 × 10⁹⁷(98-digit number)
11304968809037263569…94435002632291706879
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:57,785,083 XPM·at block #6,817,628 · updates every 60s
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