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Block #3,504,653

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/8/2020, 1:49:15 AM · Difficulty 10.9307 · 3,336,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6e2d46e7998614a4f72fc66df9872f60c3a69d98a81a746259aee0ec5f1da085

View on Chainz ↗

Height

#3,504,653

Difficulty

10.930704

Transactions

Size

424 B

Version

Bits

0aee42a1

Nonce

1,208,568,155

Timestamp

1/8/2020, 1:49:15 AM

Confirmations

3,336,750

Merkle Root

9f791266f0a00e9e6a1fb4a3c6bb47ff67041bb3ac2c059933192f3265d25381

Transactions (2)

Coinbase6c8d7e8aabbcad…151438f8163e4b

1 in → 1 out8.3700 XPM110 B

ASiq2qtK…VMhmk7yL

447e259c537ef4…46501c2cdd0e30

1 in → 2 out1.2989 XPM225 B

AUA38Ys3…uBfJ1V6B ASiq2qtK…VMhmk7yL

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.

6.507 × 10⁹¹(92-digit number)

65072496275961944859…79218004142670343600

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

6.507 × 10⁹¹(92-digit number)

65072496275961944859…79218004142670343599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.507 × 10⁹¹(92-digit number)

65072496275961944859…79218004142670343601

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

1.301 × 10⁹²(93-digit number)

13014499255192388971…58436008285340687199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.301 × 10⁹²(93-digit number)

13014499255192388971…58436008285340687201

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

2.602 × 10⁹²(93-digit number)

26028998510384777943…16872016570681374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.602 × 10⁹²(93-digit number)

26028998510384777943…16872016570681374401

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

5.205 × 10⁹²(93-digit number)

52057997020769555887…33744033141362748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.205 × 10⁹²(93-digit number)

52057997020769555887…33744033141362748801

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

1.041 × 10⁹³(94-digit number)

10411599404153911177…67488066282725497599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.041 × 10⁹³(94-digit number)

10411599404153911177…67488066282725497601

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

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 3504653

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 6e2d46e7998614a4f72fc66df9872f60c3a69d98a81a746259aee0ec5f1da085

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 #3,504,653 on Chainz ↗

Block #3,504,653

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