Home/Chain Registry/Block #403,890

Block #403,890

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/14/2014, 11:39:48 AM · Difficulty 10.4326 · 6,408,992 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1d0a3cd02e4821d079285202d435b144d7931376e0eceabd7aaaaaa19def4e66

View on Chainz ↗

Height

#403,890

Difficulty

10.432574

Transactions

Size

1.57 KB

Version

Bits

0a6ebd24

Nonce

237,482

Timestamp

2/14/2014, 11:39:48 AM

Confirmations

6,408,992

Merkle Root

da95cf288f5220bbbc634116280dd194a7a3391f927014e6833b5e3eeb0e50be

Transactions (4)

Coinbase2495a0f09d2902…012a403ebf0c34

1 in → 23 out9.1700 XPM845 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AYtDvcGs…VuAcA7m7 AGKhfQo2…h7fBXLX6 AYRvXuTr…CkbwFeLY

c314010bde21b4…b7d2782ec6b7a4

1 in → 2 out9.1700 XPM224 B

AHSEFiHR…nAfau8Wb AdQnBKM4…zozpvqnU

b2a50bce52fce4…86db5f8aed75c8

1 in → 2 out9.1700 XPM226 B

AefmWfNc…jafhDVdH AVhKUH76…CVMq3p46

a0db7f6fa40fba…725584e2c078d4

1 in → 2 out7.1462 XPM225 B

AcSHtsXN…cSSZbzQd AKqpuDaj…QY1QNWsD

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.

2.529 × 10⁹⁶(97-digit number)

25293175111440380171…07932106438892450110

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

2.529 × 10⁹⁶(97-digit number)

25293175111440380171…07932106438892450109

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.529 × 10⁹⁶(97-digit number)

25293175111440380171…07932106438892450111

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

5.058 × 10⁹⁶(97-digit number)

50586350222880760342…15864212877784900219

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.058 × 10⁹⁶(97-digit number)

50586350222880760342…15864212877784900221

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

1.011 × 10⁹⁷(98-digit number)

10117270044576152068…31728425755569800439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.011 × 10⁹⁷(98-digit number)

10117270044576152068…31728425755569800441

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

2.023 × 10⁹⁷(98-digit number)

20234540089152304136…63456851511139600879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.023 × 10⁹⁷(98-digit number)

20234540089152304136…63456851511139600881

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

4.046 × 10⁹⁷(98-digit number)

40469080178304608273…26913703022279201759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.046 × 10⁹⁷(98-digit number)

40469080178304608273…26913703022279201761

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 403890

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 1d0a3cd02e4821d079285202d435b144d7931376e0eceabd7aaaaaa19def4e66

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 #403,890 on Chainz ↗

Block #403,890

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