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Block #879,459

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/2/2015, 4:53:10 PM · Difficulty 10.9625 · 5,952,897 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ebb4a401c5b83a2eec9a292a38e236c47b1982ebe10ceb3265deecfeaced7d58

View on Chainz ↗

Height

#879,459

Difficulty

10.962549

Transactions

Size

1.15 KB

Version

Bits

0af66995

Nonce

604,052,712

Timestamp

1/2/2015, 4:53:10 PM

Confirmations

5,952,897

Merkle Root

a8fce37e6fd423a732bc3348add763c8029b11b93591db0bb7af2897445569b4

Transactions (4)

Coinbase858d39589c26c6…43cc7e361876ef

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

7aa0ae8501130d…728e7fad098040

1 in → 2 out8.2900 XPM227 B

AHRoBSh4…BSVTQ36Q AcwRM9pP…zvF16MWn

b5abe8482fea1d…59b32c0679fdf5

1 in → 2 out8.2900 XPM225 B

AGUyqfi6…Pz4SzsJ1 AFv8jiXE…b4pgdkLW

5de15153f5bd0c…8ff868bd9dc370

3 in → 2 out2.3588 XPM521 B

ALP6szJY…eEPSo5sX AJ9DmqD2…CcLrYJ1p

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.

1.564 × 10⁹⁶(97-digit number)

15646198628928688207…24116011200153717280

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

1.564 × 10⁹⁶(97-digit number)

15646198628928688207…24116011200153717279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.564 × 10⁹⁶(97-digit number)

15646198628928688207…24116011200153717281

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

3.129 × 10⁹⁶(97-digit number)

31292397257857376414…48232022400307434559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.129 × 10⁹⁶(97-digit number)

31292397257857376414…48232022400307434561

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

6.258 × 10⁹⁶(97-digit number)

62584794515714752829…96464044800614869119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.258 × 10⁹⁶(97-digit number)

62584794515714752829…96464044800614869121

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

1.251 × 10⁹⁷(98-digit number)

12516958903142950565…92928089601229738239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.251 × 10⁹⁷(98-digit number)

12516958903142950565…92928089601229738241

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

2.503 × 10⁹⁷(98-digit number)

25033917806285901131…85856179202459476479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.503 × 10⁹⁷(98-digit number)

25033917806285901131…85856179202459476481

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 879459

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 ebb4a401c5b83a2eec9a292a38e236c47b1982ebe10ceb3265deecfeaced7d58

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 #879,459 on Chainz ↗

Block #879,459

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