Home/Chain Registry/Block #270,917

Block #270,917

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/24/2013, 7:29:52 AM · Difficulty 9.9514 · 6,569,319 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

189e47fb2d3686b09f7e41ad2ad0e52fa3249b0a9c53ff395481d2f35f2b4795

View on Chainz ↗

Height

#270,917

Difficulty

9.951373

Transactions

Size

1.43 KB

Version

Bits

09f38d34

Nonce

67,460

Timestamp

11/24/2013, 7:29:52 AM

Confirmations

6,569,319

Merkle Root

ca50a91120d33d30c7d80a075b31598821bb8a37188be931330713d63fafb48d

Transactions (4)

Coinbaseffb3bbe49a611f…5ba2a51af396a8

1 in → 1 out10.1100 XPM109 B

AH5nZqzC…pz6JwD6g

a0fd475a908c2e…2e8afff272128f

3 in → 2 out32.0102 XPM523 B

AecDACjw…rafuP9dw AJR9XuYK…uGFLH2rG

8eac12052b93ba…c1284abc711990

1 in → 2 out10.0500 XPM226 B

APbkRgvu…jjNGjdXP AXSb7FDm…FQaNqgSb

cd4d22bb7e98d6…35d81ff8a74981

3 in → 2 out2.0195 XPM520 B

Aby9C38D…VfMWBSia AVC4o9v9…qLxb8oqT

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.

3.310 × 10⁹⁷(98-digit number)

33105834630648844200…72677549366043310080

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

3.310 × 10⁹⁷(98-digit number)

33105834630648844200…72677549366043310079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.310 × 10⁹⁷(98-digit number)

33105834630648844200…72677549366043310081

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

6.621 × 10⁹⁷(98-digit number)

66211669261297688400…45355098732086620159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.621 × 10⁹⁷(98-digit number)

66211669261297688400…45355098732086620161

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

1.324 × 10⁹⁸(99-digit number)

13242333852259537680…90710197464173240319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.324 × 10⁹⁸(99-digit number)

13242333852259537680…90710197464173240321

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

2.648 × 10⁹⁸(99-digit number)

26484667704519075360…81420394928346480639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.648 × 10⁹⁸(99-digit number)

26484667704519075360…81420394928346480641

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

5.296 × 10⁹⁸(99-digit number)

52969335409038150720…62840789856692961279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

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 270917

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 189e47fb2d3686b09f7e41ad2ad0e52fa3249b0a9c53ff395481d2f35f2b4795

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 #270,917 on Chainz ↗

Block #270,917

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