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Block #2,668,906

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/19/2018, 9:10:17 PM · Difficulty 11.6768 · 4,167,999 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

2edecb40682b32664458faa38dd10a961ef6f53bfaf620a9d3f1ede4be62570e

View on Chainz ↗

Height

#2,668,906

Difficulty

11.676837

Transactions

Size

987 B

Version

Bits

0bad452f

Nonce

629,941,796

Timestamp

5/19/2018, 9:10:17 PM

Confirmations

4,167,999

Merkle Root

5a6f254f49c73e63034084838f5643a0a83360f70c4a8fcd7ff1d720149965be

Transactions (2)

Coinbase860ccaaddac9b7…3020cf62f0bc27

1 in → 1 out7.3300 XPM110 B

AUkN5jTy…XerzD8jN

8ec7dd5228da4d…00a4de53343723

5 in → 2 out8.8150 XPM785 B

AagJAtLi…KHTQE8vJ AK7Cw8FY…f65no6y7

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.

2.863 × 10⁹⁸(99-digit number)

28630252259219605274…52178242007052124160

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 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.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

2.863 × 10⁹⁸(99-digit number)

28630252259219605274…52178242007052124159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.863 × 10⁹⁸(99-digit number)

28630252259219605274…52178242007052124161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

5.726 × 10⁹⁸(99-digit number)

57260504518439210549…04356484014104248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.726 × 10⁹⁸(99-digit number)

57260504518439210549…04356484014104248321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.145 × 10⁹⁹(100-digit number)

11452100903687842109…08712968028208496639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.145 × 10⁹⁹(100-digit number)

11452100903687842109…08712968028208496641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

2.290 × 10⁹⁹(100-digit number)

22904201807375684219…17425936056416993279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.290 × 10⁹⁹(100-digit number)

22904201807375684219…17425936056416993281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

4.580 × 10⁹⁹(100-digit number)

45808403614751368439…34851872112833986559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.580 × 10⁹⁹(100-digit number)

45808403614751368439…34851872112833986561

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.161 × 10⁹⁹(100-digit number)

91616807229502736878…69703744225667973119

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 Bi-Twin Chain. 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.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

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 TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2668906

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock 2edecb40682b32664458faa38dd10a961ef6f53bfaf620a9d3f1ede4be62570e

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,668,906 on Chainz ↗

Block #2,668,906

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