Home/Chain Registry/Block #318,254

Block #318,254

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/18/2013, 5:52:01 AM · Difficulty 10.1595 · 6,493,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44e46cf879d47a6c082d6415e48a7ae09e3a2e1aa360b495107ab364be393a1a

View on Chainz ↗

Height

#318,254

Difficulty

10.159546

Transactions

Size

1.04 KB

Version

Bits

0a28d807

Nonce

216,845

Timestamp

12/18/2013, 5:52:01 AM

Confirmations

6,493,496

Merkle Root

cad2bcbe43378f7eb3656892bd5e114e17d49efd9f7d38a64b3260947cc248a6

Transactions (1)

Coinbasecad2bcbe43378f…3260947cc248a6

1 in → 27 out9.6700 XPM981 B

Ad9pSzHt…cpJ3y2zz Aac9Hjdg…P4ktypc3 AZemWJAo…6jhDtieG AZ2pPuKg…95SN2Yr7 AJzWx2VD…j4ZSMit5

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.

1.710 × 10⁹³(94-digit number)

17101924610592327108…57924567068113436450

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

1.710 × 10⁹³(94-digit number)

17101924610592327108…57924567068113436449

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.710 × 10⁹³(94-digit number)

17101924610592327108…57924567068113436451

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

3.420 × 10⁹³(94-digit number)

34203849221184654216…15849134136226872899

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.420 × 10⁹³(94-digit number)

34203849221184654216…15849134136226872901

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

6.840 × 10⁹³(94-digit number)

68407698442369308433…31698268272453745799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.840 × 10⁹³(94-digit number)

68407698442369308433…31698268272453745801

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

1.368 × 10⁹⁴(95-digit number)

13681539688473861686…63396536544907491599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.368 × 10⁹⁴(95-digit number)

13681539688473861686…63396536544907491601

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

2.736 × 10⁹⁴(95-digit number)

27363079376947723373…26793073089814983199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.736 × 10⁹⁴(95-digit number)

27363079376947723373…26793073089814983201

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 318254

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 44e46cf879d47a6c082d6415e48a7ae09e3a2e1aa360b495107ab364be393a1a

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 #318,254 on Chainz ↗

Block #318,254

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