Home/Chain Registry/Block #369,074

Block #369,074

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 3:59:55 AM · Difficulty 10.4443 · 6,457,700 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d89a857e3095f815f8f0a3ab01925a8f372fb8407c5b5668775c9beb3778bd69

View on Chainz ↗

Height

#369,074

Difficulty

10.444288

Transactions

Size

2.56 KB

Version

Bits

0a71bcd8

Nonce

165,812

Timestamp

1/21/2014, 3:59:55 AM

Confirmations

6,457,700

Merkle Root

f3faf9c762ce63dc27ede873fcd68536429b2fe9434bbf8ff92816994ef09a8b

Transactions (3)

Coinbase9e1a081d14a356…c8ad2d7995b5de

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

916a88036f99f8…7593bae3a928db

1 in → 1 out9.1800 XPM158 B

AYFCsYhj…NXHomGMr

6ed42c66916a86…d3c0ddcfa064cc

15 in → 1 out4.9003 XPM2.21 KB

ALZJxDHK…MxEk6SeC

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.

1.314 × 10⁹⁵(96-digit number)

13145533990950588168…03706601728428029440

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

1.314 × 10⁹⁵(96-digit number)

13145533990950588168…03706601728428029439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.314 × 10⁹⁵(96-digit number)

13145533990950588168…03706601728428029441

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

2.629 × 10⁹⁵(96-digit number)

26291067981901176336…07413203456856058879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.629 × 10⁹⁵(96-digit number)

26291067981901176336…07413203456856058881

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

5.258 × 10⁹⁵(96-digit number)

52582135963802352672…14826406913712117759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.258 × 10⁹⁵(96-digit number)

52582135963802352672…14826406913712117761

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

1.051 × 10⁹⁶(97-digit number)

10516427192760470534…29652813827424235519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.051 × 10⁹⁶(97-digit number)

10516427192760470534…29652813827424235521

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

2.103 × 10⁹⁶(97-digit number)

21032854385520941068…59305627654848471039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.103 × 10⁹⁶(97-digit number)

21032854385520941068…59305627654848471041

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 369074

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 d89a857e3095f815f8f0a3ab01925a8f372fb8407c5b5668775c9beb3778bd69

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 #369,074 on Chainz ↗

Block #369,074

Cookie Preferences