Home/Chain Registry/Block #298,684

Block #298,684

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/7/2013, 11:50:51 AM · Difficulty 9.9920 · 6,515,301 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a0b80c0acde56d40bd85c6528f920fc73a0c27c0602bf33ef8204b580aa528eb

View on Chainz ↗

Height

#298,684

Difficulty

9.991990

Transactions

Size

1.18 KB

Version

Bits

09fdf30d

Nonce

596,915

Timestamp

12/7/2013, 11:50:51 AM

Confirmations

6,515,301

Merkle Root

8f56eda7615eba01b988880bda13824f371a8801986dbf742237facb0668d5ac

Transactions (1)

Coinbase8f56eda7615eba…37facb0668d5ac

1 in → 31 out9.9800 XPM1.09 KB

Ad9pSzHt…cpJ3y2zz ASWX42VM…XypQABkY AcM3ext6…Hwtj9Qp3 AMdvB6BS…DPq9FYdA AawixgFr…3Cd95Uu2

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.

1.165 × 10⁹⁷(98-digit number)

11654814512527529869…87768074327410803200

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

1.165 × 10⁹⁷(98-digit number)

11654814512527529869…87768074327410803199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.165 × 10⁹⁷(98-digit number)

11654814512527529869…87768074327410803201

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

2.330 × 10⁹⁷(98-digit number)

23309629025055059738…75536148654821606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.330 × 10⁹⁷(98-digit number)

23309629025055059738…75536148654821606401

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

4.661 × 10⁹⁷(98-digit number)

46619258050110119477…51072297309643212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.661 × 10⁹⁷(98-digit number)

46619258050110119477…51072297309643212801

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

9.323 × 10⁹⁷(98-digit number)

93238516100220238954…02144594619286425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.323 × 10⁹⁷(98-digit number)

93238516100220238954…02144594619286425601

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

1.864 × 10⁹⁸(99-digit number)

18647703220044047790…04289189238572851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.864 × 10⁹⁸(99-digit number)

18647703220044047790…04289189238572851201

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 298684

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 a0b80c0acde56d40bd85c6528f920fc73a0c27c0602bf33ef8204b580aa528eb

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 #298,684 on Chainz ↗

Block #298,684

Cookie Preferences