Home/Chain Registry/Block #360,465

Block #360,465

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 11:27:38 AM · Difficulty 10.3932 · 6,441,006 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3a03104f5c6ae4aeae12d5a5b779ca925137371c67d4302769d3f3fc43eaa3e3

View on Chainz ↗

Height

#360,465

Difficulty

10.393225

Transactions

Size

870 B

Version

Bits

0a64aa61

Nonce

63,243

Timestamp

1/15/2014, 11:27:38 AM

Confirmations

6,441,006

Merkle Root

e32247edf8a4049b2fdb30239277f965076880e0082bc52affaaf518a4cde8c0

Transactions (4)

Coinbase5f2c0733ea95da…d00a6e4d1850be

1 in → 1 out9.2700 XPM100 B

AaXb6Ldz…XefG91jF

f23e256b4a8342…56d1ccabc72b11

1 in → 2 out2.4044 XPM226 B

AeDFWfLr…ocqM5DJT AYGNkhZK…5RcfjfZH

e8951d312dad68…ffe0bc925315de

1 in → 2 out2.0892 XPM225 B

AZT5X1Zo…ZuUSq36R AeGkrx8m…V3akuHL7

ab80936c108e15…bb8ac996a8fc21

1 in → 2 out2.3403 XPM226 B

Ad8k9vEa…bRCFABxw ARVHk3CY…fXAXLJH3

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.

1.772 × 10¹⁰¹(102-digit number)

17721546060838551934…75395956401540516160

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

1.772 × 10¹⁰¹(102-digit number)

17721546060838551934…75395956401540516159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.772 × 10¹⁰¹(102-digit number)

17721546060838551934…75395956401540516161

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

3.544 × 10¹⁰¹(102-digit number)

35443092121677103869…50791912803081032319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.544 × 10¹⁰¹(102-digit number)

35443092121677103869…50791912803081032321

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

7.088 × 10¹⁰¹(102-digit number)

70886184243354207739…01583825606162064639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.088 × 10¹⁰¹(102-digit number)

70886184243354207739…01583825606162064641

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

1.417 × 10¹⁰²(103-digit number)

14177236848670841547…03167651212324129279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.417 × 10¹⁰²(103-digit number)

14177236848670841547…03167651212324129281

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

2.835 × 10¹⁰²(103-digit number)

28354473697341683095…06335302424648258559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.835 × 10¹⁰²(103-digit number)

28354473697341683095…06335302424648258561

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 360465

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 3a03104f5c6ae4aeae12d5a5b779ca925137371c67d4302769d3f3fc43eaa3e3

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 #360,465 on Chainz ↗