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Block #362,979

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/17/2014, 2:32:23 AM · Difficulty 10.4147 · 6,476,022 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

71727e48446cd8e044aeec089b3a7bec08af455b5a4029ddd19b05a79c52f54e

View on Chainz ↗

Height

#362,979

Difficulty

10.414713

Transactions

Size

1.23 KB

Version

Bits

0a6a2aa3

Nonce

225,052

Timestamp

1/17/2014, 2:32:23 AM

Confirmations

6,476,022

Merkle Root

31556e338d8530bce21d7b62573d6736de61c919f91f12581b1ddc265d084627

Transactions (2)

Coinbasef949563bcc6ccf…0a731a886eda6d

1 in → 26 out9.2100 XPM947 B

Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 Ad9pSzHt…cpJ3y2zz AZV4TwxQ…8JnQqSoH AZemWJAo…6jhDtieG

31946305c0e7fc…f186228557bde4

1 in → 2 out2.9586 XPM226 B

AKN7CcHq…xmjsP77z AKKoMa7P…tofb1RZy

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.

1.445 × 10⁹⁵(96-digit number)

14453745984807919919…04396027530617528800

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

1.445 × 10⁹⁵(96-digit number)

14453745984807919919…04396027530617528799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.445 × 10⁹⁵(96-digit number)

14453745984807919919…04396027530617528801

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

2.890 × 10⁹⁵(96-digit number)

28907491969615839839…08792055061235057599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.890 × 10⁹⁵(96-digit number)

28907491969615839839…08792055061235057601

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

5.781 × 10⁹⁵(96-digit number)

57814983939231679678…17584110122470115199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.781 × 10⁹⁵(96-digit number)

57814983939231679678…17584110122470115201

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

1.156 × 10⁹⁶(97-digit number)

11562996787846335935…35168220244940230399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.156 × 10⁹⁶(97-digit number)

11562996787846335935…35168220244940230401

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

2.312 × 10⁹⁶(97-digit number)

23125993575692671871…70336440489880460799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.312 × 10⁹⁶(97-digit number)

23125993575692671871…70336440489880460801

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 362979

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 71727e48446cd8e044aeec089b3a7bec08af455b5a4029ddd19b05a79c52f54e

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 #362,979 on Chainz ↗

Block #362,979

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