Home/Chain Registry/Block #440,150

Block #440,150

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/12/2014, 5:41:50 AM · Difficulty 10.3515 · 6,351,186 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4b1f5655409d0ed9cd25dfd58e80bbe260d6aedb627e691d49a131300fa49ec7

View on Chainz ↗

Height

#440,150

Difficulty

10.351547

Transactions

Size

9.08 KB

Version

Bits

0a59fefc

Nonce

82,208

Timestamp

3/12/2014, 5:41:50 AM

Confirmations

6,351,186

Merkle Root

95b1ae66c9d68d53f29ed15d9248df11abc9fb4434c1a5857f762e9e2531bc94

Transactions (4)

Coinbasedfb1854bba2d94…9ae681611b6f3e

1 in → 24 out9.3200 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AScAzqGc…BZ6tV1vJ AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn

b5f91b2058c2c6…438d048a2a4ac4

25 in → 2 out14.0381 XPM3.69 KB

AHGjT5FG…7ApbeqmU AGMoLVR4…p3b74SMx

72284695f6094a…b8a50e7a031412

28 in → 2 out15.0734 XPM4.13 KB

Ae8Poxqu…vwiqDMMv AHGjT5FG…7ApbeqmU

dcf5a64de2a7e6…fe41be4dc026ca

1 in → 5 out19.0567 XPM328 B

AJVJtuAj…bqEFTaUx AZAYcqyP…Bf5uQ6gQ AJMYfNh6…W6UWWALu ATZwJtyx…rFnv3nK8 AGxYGYHa…FRp3G4Gh

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.

3.372 × 10⁹¹(92-digit number)

33725266321987640248…02265570718026712800

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

3.372 × 10⁹¹(92-digit number)

33725266321987640248…02265570718026712799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.372 × 10⁹¹(92-digit number)

33725266321987640248…02265570718026712801

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

6.745 × 10⁹¹(92-digit number)

67450532643975280496…04531141436053425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.745 × 10⁹¹(92-digit number)

67450532643975280496…04531141436053425601

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

1.349 × 10⁹²(93-digit number)

13490106528795056099…09062282872106851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.349 × 10⁹²(93-digit number)

13490106528795056099…09062282872106851201

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

2.698 × 10⁹²(93-digit number)

26980213057590112198…18124565744213702399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.698 × 10⁹²(93-digit number)

26980213057590112198…18124565744213702401

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

5.396 × 10⁹²(93-digit number)

53960426115180224396…36249131488427404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.396 × 10⁹²(93-digit number)

53960426115180224396…36249131488427404801

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 440150

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 4b1f5655409d0ed9cd25dfd58e80bbe260d6aedb627e691d49a131300fa49ec7

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 #440,150 on Chainz ↗