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Block #445,904

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/16/2014, 5:07:12 AM · Difficulty 10.3590 · 6,351,964 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c1ba7e924a5c08d2f68be676b0f6ca0a3b2245c7c294d998a7db2460bab3422f

View on Chainz ↗

Height

#445,904

Difficulty

10.359048

Transactions

Size

1.17 KB

Version

Bits

0a5bea94

Nonce

258

Timestamp

3/16/2014, 5:07:12 AM

Confirmations

6,351,964

Merkle Root

9967b287afaef6dc5cdf68dc8cf7e3ab600f4ce61caf88584ff94fed8852b4bb

Transactions (2)

Coinbase5678b62a6985c3…5e2d5942557228

1 in → 1 out9.3100 XPM116 B

AbwWkWZt…kawDhufa

d1f981b4fca135…bb6e007ef6aee2

5 in → 10 out29.0567 XPM990 B

ATAxh43K…62WhpjvU AJrZAsFD…mqWWUUnE AeKNrjNj…1NEq95Ta AcGCmc9D…1fUXRBUx APkSf5C5…wYwrjSQa

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.

1.540 × 10⁹⁷(98-digit number)

15401051723687434678…90924861590296825250

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

1.540 × 10⁹⁷(98-digit number)

15401051723687434678…90924861590296825249

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.540 × 10⁹⁷(98-digit number)

15401051723687434678…90924861590296825251

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

3.080 × 10⁹⁷(98-digit number)

30802103447374869356…81849723180593650499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.080 × 10⁹⁷(98-digit number)

30802103447374869356…81849723180593650501

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

6.160 × 10⁹⁷(98-digit number)

61604206894749738713…63699446361187300999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.160 × 10⁹⁷(98-digit number)

61604206894749738713…63699446361187301001

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

1.232 × 10⁹⁸(99-digit number)

12320841378949947742…27398892722374601999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.232 × 10⁹⁸(99-digit number)

12320841378949947742…27398892722374602001

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

2.464 × 10⁹⁸(99-digit number)

24641682757899895485…54797785444749203999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.464 × 10⁹⁸(99-digit number)

24641682757899895485…54797785444749204001

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 445904

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 c1ba7e924a5c08d2f68be676b0f6ca0a3b2245c7c294d998a7db2460bab3422f

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 #445,904 on Chainz ↗