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Block #350,531

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 3:10:43 AM · Difficulty 10.2857 · 6,476,839 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ef996ab1fae62160faf0aeffe3f941430d80f33b18896bf7dd5de81b1cdcf3be

View on Chainz ↗

Height

#350,531

Difficulty

10.285742

Transactions

Size

357 B

Version

Bits

0a49265e

Nonce

1,062,391

Timestamp

1/9/2014, 3:10:43 AM

Confirmations

6,476,839

Merkle Root

663d6e2051248e8e4eb825f266eeede8078b02f19894846b90e8abee75ecbc81

Transactions (1)

Coinbase663d6e2051248e…e8abee75ecbc81

1 in → 6 out9.4400 XPM267 B

AMQC4aya…c4ptxi3K Ac9ofGgC…KaPzHH7W AWARJTEj…iSsb435H AefYHMGV…kXeAreZn AXHBNbJ2…45RYZMFg

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.

7.273 × 10⁹⁴(95-digit number)

72730926523941979806…02222937789116309450

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

7.273 × 10⁹⁴(95-digit number)

72730926523941979806…02222937789116309449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.273 × 10⁹⁴(95-digit number)

72730926523941979806…02222937789116309451

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

1.454 × 10⁹⁵(96-digit number)

14546185304788395961…04445875578232618899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.454 × 10⁹⁵(96-digit number)

14546185304788395961…04445875578232618901

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

2.909 × 10⁹⁵(96-digit number)

29092370609576791922…08891751156465237799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.909 × 10⁹⁵(96-digit number)

29092370609576791922…08891751156465237801

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

5.818 × 10⁹⁵(96-digit number)

58184741219153583844…17783502312930475599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.818 × 10⁹⁵(96-digit number)

58184741219153583844…17783502312930475601

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

1.163 × 10⁹⁶(97-digit number)

11636948243830716768…35567004625860951199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.163 × 10⁹⁶(97-digit number)

11636948243830716768…35567004625860951201

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 350531

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 ef996ab1fae62160faf0aeffe3f941430d80f33b18896bf7dd5de81b1cdcf3be

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 #350,531 on Chainz ↗

Block #350,531

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