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Block #447,311

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/17/2014, 5:13:15 AM · Difficulty 10.3542 · 6,379,495 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb5d51e21694ba138d061ad90be743051a3d5e9140d2bb681c2d9eaf3fbadd6d

View on Chainz ↗

Height

#447,311

Difficulty

10.354155

Transactions

Size

970 B

Version

Bits

0a5aa9e0

Nonce

23,157

Timestamp

3/17/2014, 5:13:15 AM

Confirmations

6,379,495

Merkle Root

9c61d94ce184dab7cdf5e4c4828ff19326fe47f7848588fefe0b5f665c5690a1

Transactions (1)

Coinbase9c61d94ce184da…0b5f665c5690a1

1 in → 24 out9.3100 XPM879 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw ASgUri65…C7NLcyBg AcuM7XiJ…5uND8Jce AbPcCMg4…719q6mAX

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.

6.733 × 10⁹⁷(98-digit number)

67332634437282575186…04906332825968608800

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

6.733 × 10⁹⁷(98-digit number)

67332634437282575186…04906332825968608799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.733 × 10⁹⁷(98-digit number)

67332634437282575186…04906332825968608801

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

1.346 × 10⁹⁸(99-digit number)

13466526887456515037…09812665651937217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.346 × 10⁹⁸(99-digit number)

13466526887456515037…09812665651937217601

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

2.693 × 10⁹⁸(99-digit number)

26933053774913030074…19625331303874435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.693 × 10⁹⁸(99-digit number)

26933053774913030074…19625331303874435201

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

5.386 × 10⁹⁸(99-digit number)

53866107549826060149…39250662607748870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.386 × 10⁹⁸(99-digit number)

53866107549826060149…39250662607748870401

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

1.077 × 10⁹⁹(100-digit number)

10773221509965212029…78501325215497740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.077 × 10⁹⁹(100-digit number)

10773221509965212029…78501325215497740801

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 447311

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 eb5d51e21694ba138d061ad90be743051a3d5e9140d2bb681c2d9eaf3fbadd6d

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 #447,311 on Chainz ↗

Block #447,311

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