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Block #454,650

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/22/2014, 2:26:04 AM · Difficulty 10.3962 · 6,372,028 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ae2297e5edd6c7176df262512bbcec2a986f9cb4303f67c1cdc7b1668d6628b9

View on Chainz ↗

Height

#454,650

Difficulty

10.396214

Transactions

Size

902 B

Version

Bits

0a656e48

Nonce

601,743

Timestamp

3/22/2014, 2:26:04 AM

Confirmations

6,372,028

Merkle Root

1adee86e38f48b426ec0ee19ea7718c3faf6a9b8490658b6bdb79795c87df3e0

Transactions (1)

Coinbase1adee86e38f48b…b79795c87df3e0

1 in → 22 out9.2400 XPM811 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ATp4jJhs…TbSgR8Qb APtc8nU2…tp6qFHwW Adbb4svj…dQWTHsq5

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.

1.029 × 10⁹⁷(98-digit number)

10299580580481488439…19226566633516028800

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

1.029 × 10⁹⁷(98-digit number)

10299580580481488439…19226566633516028799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.029 × 10⁹⁷(98-digit number)

10299580580481488439…19226566633516028801

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

2.059 × 10⁹⁷(98-digit number)

20599161160962976879…38453133267032057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.059 × 10⁹⁷(98-digit number)

20599161160962976879…38453133267032057601

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

4.119 × 10⁹⁷(98-digit number)

41198322321925953758…76906266534064115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.119 × 10⁹⁷(98-digit number)

41198322321925953758…76906266534064115201

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

8.239 × 10⁹⁷(98-digit number)

82396644643851907516…53812533068128230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.239 × 10⁹⁷(98-digit number)

82396644643851907516…53812533068128230401

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

1.647 × 10⁹⁸(99-digit number)

16479328928770381503…07625066136256460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.647 × 10⁹⁸(99-digit number)

16479328928770381503…07625066136256460801

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 454650

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 ae2297e5edd6c7176df262512bbcec2a986f9cb4303f67c1cdc7b1668d6628b9

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 #454,650 on Chainz ↗

Block #454,650

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