Home/Chain Registry/Block #463,508

Block #463,508

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/28/2014, 4:37:11 AM · Difficulty 10.4133 · 6,337,335 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6922d4e4aaac28859d8ef30e43dd598c138a6d025f93af27604aede277f0036e

View on Chainz ↗

Height

#463,508

Difficulty

10.413267

Transactions

Size

2.34 KB

Version

Bits

0a69cbd7

Nonce

37,901

Timestamp

3/28/2014, 4:37:11 AM

Confirmations

6,337,335

Merkle Root

f988efed485ed2b2aefb9dd2b55d3fb595e174842d687e8ba2d2ad6d8019d83c

Transactions (2)

Coinbasee9abff631ec54b…3dd37ab13021c0

1 in → 23 out9.2300 XPM845 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw APtc8nU2…tp6qFHwW AZ34NcPy…8FPeFjPV ASgUri65…C7NLcyBg

0f8b5ed73904ee…e1832b2d83a707

7 in → 18 out58.3208 XPM1.42 KB

AMf8PhfM…AME5WSpE ALXuy3QZ…2Cojv76m AeKNrjNj…1NEq95Ta ATL8jSyw…pWnYFMfC AUi2icYo…5k64iTPM

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.

4.832 × 10⁹⁶(97-digit number)

48320906953964373600…68431975190766753660

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

4.832 × 10⁹⁶(97-digit number)

48320906953964373600…68431975190766753659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.832 × 10⁹⁶(97-digit number)

48320906953964373600…68431975190766753661

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

9.664 × 10⁹⁶(97-digit number)

96641813907928747201…36863950381533507319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.664 × 10⁹⁶(97-digit number)

96641813907928747201…36863950381533507321

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

1.932 × 10⁹⁷(98-digit number)

19328362781585749440…73727900763067014639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.932 × 10⁹⁷(98-digit number)

19328362781585749440…73727900763067014641

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

3.865 × 10⁹⁷(98-digit number)

38656725563171498880…47455801526134029279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.865 × 10⁹⁷(98-digit number)

38656725563171498880…47455801526134029281

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

7.731 × 10⁹⁷(98-digit number)

77313451126342997761…94911603052268058559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.731 × 10⁹⁷(98-digit number)

77313451126342997761…94911603052268058561

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 463508

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 6922d4e4aaac28859d8ef30e43dd598c138a6d025f93af27604aede277f0036e

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 #463,508 on Chainz ↗