Home/Chain Registry/Block #377,930

Block #377,930

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 11:28:18 AM · Difficulty 10.4206 · 6,433,776 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

859478dc2e56229d247c6f6605cc720c30cd80815f8bfadee3b8fcebbb9945fd

View on Chainz ↗

Height

#377,930

Difficulty

10.420616

Transactions

Size

203 B

Version

Bits

0a6bad83

Nonce

288,883

Timestamp

1/27/2014, 11:28:18 AM

Confirmations

6,433,776

Merkle Root

9f460d9b03f29e88fff49725a72fc16528bc01994eb6386d779c50514ee2ce80

Transactions (1)

Coinbase9f460d9b03f29e…9c50514ee2ce80

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

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.

1.394 × 10¹⁰¹(102-digit number)

13947574874547910125…47144677366584192000

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

1.394 × 10¹⁰¹(102-digit number)

13947574874547910125…47144677366584191999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.394 × 10¹⁰¹(102-digit number)

13947574874547910125…47144677366584192001

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

2.789 × 10¹⁰¹(102-digit number)

27895149749095820251…94289354733168383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.789 × 10¹⁰¹(102-digit number)

27895149749095820251…94289354733168384001

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

5.579 × 10¹⁰¹(102-digit number)

55790299498191640503…88578709466336767999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.579 × 10¹⁰¹(102-digit number)

55790299498191640503…88578709466336768001

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

1.115 × 10¹⁰²(103-digit number)

11158059899638328100…77157418932673535999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.115 × 10¹⁰²(103-digit number)

11158059899638328100…77157418932673536001

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

2.231 × 10¹⁰²(103-digit number)

22316119799276656201…54314837865347071999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.231 × 10¹⁰²(103-digit number)

22316119799276656201…54314837865347072001

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 377930

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 859478dc2e56229d247c6f6605cc720c30cd80815f8bfadee3b8fcebbb9945fd

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 #377,930 on Chainz ↗

Block #377,930

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