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Block #374,867

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 8:42:30 AM · Difficulty 10.4181 · 6,429,099 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7ad43c9ea862e797637adbea743b5b85d8f1143c8fc10dd6c205ef86d67f321c

View on Chainz ↗

Height

#374,867

Difficulty

10.418147

Transactions

Size

868 B

Version

Bits

0a6b0bac

Nonce

1,078,616

Timestamp

1/25/2014, 8:42:30 AM

Confirmations

6,429,099

Merkle Root

a18a208c1a98481a4ad8d14b57ddcc5335d9044d817f2f8ca462b0386f1c45ca

Transactions (1)

Coinbasea18a208c1a9848…62b0386f1c45ca

1 in → 21 out9.1991 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AZV4TwxQ…8JnQqSoH

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.

1.388 × 10⁹⁶(97-digit number)

13882649231950200902…80308483719910986080

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

1.388 × 10⁹⁶(97-digit number)

13882649231950200902…80308483719910986079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.388 × 10⁹⁶(97-digit number)

13882649231950200902…80308483719910986081

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

2.776 × 10⁹⁶(97-digit number)

27765298463900401805…60616967439821972159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.776 × 10⁹⁶(97-digit number)

27765298463900401805…60616967439821972161

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

5.553 × 10⁹⁶(97-digit number)

55530596927800803610…21233934879643944319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.553 × 10⁹⁶(97-digit number)

55530596927800803610…21233934879643944321

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

1.110 × 10⁹⁷(98-digit number)

11106119385560160722…42467869759287888639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.110 × 10⁹⁷(98-digit number)

11106119385560160722…42467869759287888641

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

2.221 × 10⁹⁷(98-digit number)

22212238771120321444…84935739518575777279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.221 × 10⁹⁷(98-digit number)

22212238771120321444…84935739518575777281

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 374867

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 7ad43c9ea862e797637adbea743b5b85d8f1143c8fc10dd6c205ef86d67f321c

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 #374,867 on Chainz ↗