1. #6,807,186TWN10 primes

    Bi-Twin · ⛏️ coinsforall.io

Block #1,006,623

2CCLength 11★★★☆☆

Cunningham Chain of the Second Kind · Discovered 4/8/2015, 12:57:11 AM · Difficulty 10.7348 · 5,800,564 confirmations

2CC
Cunningham Chain of the Second Kind

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

Block Header
Block Hash
08c55ea2c7ead2ffa5e9f9fd0151bb97b43c850f07a81c1a4ac58974c839493e

Height

#1,006,623

Difficulty

10.734785

Transactions

3

Size

4.11 KB

Version

2

Bits

0abc1ae6

Nonce

395,221,204

Timestamp

4/8/2015, 12:57:11 AM

Confirmations

5,800,564

Merkle Root

e1f033c134ff7cb48346996c04a21e3a26797490b161852895313e07b6c89adb
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.

3.987 × 10⁹⁵(96-digit number)
39872619910469509458…04332574242003153861
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
3.987 × 10⁹⁵(96-digit number)
39872619910469509458…04332574242003153861
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
2
2^1 × origin + 1
7.974 × 10⁹⁵(96-digit number)
79745239820939018917…08665148484006307721
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
3
2^2 × origin + 1
1.594 × 10⁹⁶(97-digit number)
15949047964187803783…17330296968012615441
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
4
2^3 × origin + 1
3.189 × 10⁹⁶(97-digit number)
31898095928375607566…34660593936025230881
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
5
2^4 × origin + 1
6.379 × 10⁹⁶(97-digit number)
63796191856751215133…69321187872050461761
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
6
2^5 × origin + 1
1.275 × 10⁹⁷(98-digit number)
12759238371350243026…38642375744100923521
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
7
2^6 × origin + 1
2.551 × 10⁹⁷(98-digit number)
25518476742700486053…77284751488201847041
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
8
2^7 × origin + 1
5.103 × 10⁹⁷(98-digit number)
51036953485400972107…54569502976403694081
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
9
2^8 × origin + 1
1.020 × 10⁹⁸(99-digit number)
10207390697080194421…09139005952807388161
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
10
2^9 × origin + 1
2.041 × 10⁹⁸(99-digit number)
20414781394160388842…18278011905614776321
Verify on FactorDB ↗Wolfram Alpha ↗
×2−1 →
11
2^10 × origin + 1
4.082 × 10⁹⁸(99-digit number)
40829562788320777685…36556023811229552641
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:57,701,508 XPM·at block #6,807,186 · updates every 60s
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