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Block #280,235

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 3:04:11 PM · Difficulty 9.9740 · 6,521,314 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fbbc091066dc941dc3c7b9103bf147b5424334cfdaaad3a964037e9a9e90f3dc

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Height

#280,235

Difficulty

9.973968

Transactions

Size

1.01 KB

Version

Bits

09f955f1

Nonce

126,194

Timestamp

11/28/2013, 3:04:11 PM

Confirmations

6,521,314

Merkle Root

340f18ca506b545f87ce5fe38ae7dcd65c7ed5cfa00cf9df94a47901c783e4b5

Transactions (1)

Coinbase340f18ca506b54…a47901c783e4b5

1 in → 26 out10.0400 XPM947 B

AGFAJ5YL…ZEnBbk6G AWXYBWKP…qQAoisBJ AN63YyQR…1tfe566A AMdvB6BS…DPq9FYdA AYrgZtF4…6oLCC7XK

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.

2.540 × 10⁹⁵(96-digit number)

25408642784691380903…00847266094686424500

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

2.540 × 10⁹⁵(96-digit number)

25408642784691380903…00847266094686424499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.540 × 10⁹⁵(96-digit number)

25408642784691380903…00847266094686424501

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

5.081 × 10⁹⁵(96-digit number)

50817285569382761807…01694532189372848999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.081 × 10⁹⁵(96-digit number)

50817285569382761807…01694532189372849001

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

1.016 × 10⁹⁶(97-digit number)

10163457113876552361…03389064378745697999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.016 × 10⁹⁶(97-digit number)

10163457113876552361…03389064378745698001

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

2.032 × 10⁹⁶(97-digit number)

20326914227753104722…06778128757491395999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.032 × 10⁹⁶(97-digit number)

20326914227753104722…06778128757491396001

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

4.065 × 10⁹⁶(97-digit number)

40653828455506209445…13556257514982791999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.065 × 10⁹⁶(97-digit number)

40653828455506209445…13556257514982792001

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 280235

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 fbbc091066dc941dc3c7b9103bf147b5424334cfdaaad3a964037e9a9e90f3dc

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 #280,235 on Chainz ↗