Home/Chain Registry/Block #358,673

Block #358,673

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/14/2014, 6:46:49 AM · Difficulty 10.3840 · 6,437,638 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f8e65a727e87e82de4ebf8f70fd691e8cb29dde75d4595c517bc77ee95e1a7d0

View on Chainz ↗

Height

#358,673

Difficulty

10.384047

Transactions

Size

1.93 KB

Version

Bits

0a6250ec

Nonce

67,110,192

Timestamp

1/14/2014, 6:46:49 AM

Confirmations

6,437,638

Merkle Root

712c4c5865d93a55e1d5be52fae16c791deab28f789096ad8534cb2fd1629e67

Transactions (4)

Coinbasec65f21ec1bdf22…56309a09f2fd72

1 in → 1 out9.3000 XPM116 B

AbwWkWZt…kawDhufa

88552375901637…782cb79a6787dd

2 in → 2 out2.0001 XPM375 B

AQrDWoMi…SmAMx9nh APEdKgAQ…tbVumySg

519a7e34949928…c57716a5b8dc6b

4 in → 5 out3.5136 XPM772 B

AS4CfFYA…ksiezrwM APMQHczZ…txdGyehm AbjvDWgc…tJA7aUoJ AQhMzWVC…wfpJe2JS AQd5E7UP…cVYMAWRb

a6972b86412d36…f48f1cb96f4a73

3 in → 5 out3.5987 XPM623 B

AQd5E7UP…cVYMAWRb AS4CfFYA…ksiezrwM AQhMzWVC…wfpJe2JS AbjvDWgc…tJA7aUoJ AaqsH5Ep…U34mKBdj

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.

5.965 × 10⁹⁴(95-digit number)

59657278039250360392…88242738055173982850

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

5.965 × 10⁹⁴(95-digit number)

59657278039250360392…88242738055173982849

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.965 × 10⁹⁴(95-digit number)

59657278039250360392…88242738055173982851

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

1.193 × 10⁹⁵(96-digit number)

11931455607850072078…76485476110347965699

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.193 × 10⁹⁵(96-digit number)

11931455607850072078…76485476110347965701

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

2.386 × 10⁹⁵(96-digit number)

23862911215700144157…52970952220695931399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.386 × 10⁹⁵(96-digit number)

23862911215700144157…52970952220695931401

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

4.772 × 10⁹⁵(96-digit number)

47725822431400288314…05941904441391862799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.772 × 10⁹⁵(96-digit number)

47725822431400288314…05941904441391862801

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

9.545 × 10⁹⁵(96-digit number)

95451644862800576628…11883808882783725599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.545 × 10⁹⁵(96-digit number)

95451644862800576628…11883808882783725601

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.909 × 10⁹⁶(97-digit number)

19090328972560115325…23767617765567451199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 358673

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 f8e65a727e87e82de4ebf8f70fd691e8cb29dde75d4595c517bc77ee95e1a7d0

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 #358,673 on Chainz ↗