1. #6,802,5841CC11 primes

    Cunningham 1st · ⛏️ coinsforall.io

Block #792,255

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 11/1/2014, 2:06:08 PM · Difficulty 10.9735 · 6,010,330 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
bbf9d14b0e1a62990c62207fd6389777517dc5977b47b7a0e89bcff5e40308d1

Height

#792,255

Difficulty

10.973487

Transactions

3

Size

658 B

Version

2

Bits

0af9366e

Nonce

541,075,555

Timestamp

11/1/2014, 2:06:08 PM

Confirmations

6,010,330

Merkle Root

9870d9178eb1d02b6445f18001fb74a3334079b4abe48de92a763c046709cc1c
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.

1.758 × 10⁹⁴(95-digit number)
17587027771119328778…89760229973839300541
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
1.758 × 10⁹⁴(95-digit number)
17587027771119328778…89760229973839300541
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
3.517 × 10⁹⁴(95-digit number)
35174055542238657556…79520459947678601081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
7.034 × 10⁹⁴(95-digit number)
70348111084477315113…59040919895357202161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
1.406 × 10⁹⁵(96-digit number)
14069622216895463022…18081839790714404321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
2.813 × 10⁹⁵(96-digit number)
28139244433790926045…36163679581428808641
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
5.627 × 10⁹⁵(96-digit number)
56278488867581852090…72327359162857617281
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
1.125 × 10⁹⁶(97-digit number)
11255697773516370418…44654718325715234561
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
2.251 × 10⁹⁶(97-digit number)
22511395547032740836…89309436651430469121
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
4.502 × 10⁹⁶(97-digit number)
45022791094065481672…78618873302860938241
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
9.004 × 10⁹⁶(97-digit number)
90045582188130963345…57237746605721876481
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
1.800 × 10⁹⁷(98-digit number)
18009116437626192669…14475493211443752961
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 consecutive prime numbers forming a Cunningham Chain of the Second 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 2CC formula:

2CC: p₁ (first prime), p₂ = 2p₁ − 1, p₃ = 2p₂ − 1, …
Circulating Supply:57,664,698 XPM·at block #6,802,584 · updates every 60s
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