Home/Chain Registry/Block #135,380

Block #135,380

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 2:29:17 PM · Difficulty 9.8101 · 6,656,273 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5865b7bb7f9761b04053094ce382d060c43ef7a57e3b43caeee573392a66a2a2

View on Chainz ↗

Height

#135,380

Difficulty

9.810100

Transactions

Size

200 B

Version

Bits

09cf62b5

Nonce

478,536

Timestamp

8/26/2013, 2:29:17 PM

Confirmations

6,656,273

Merkle Root

f7a480df7d3554f7727816d50ea1bc239a1e405b0397e4db54a68d9a146a1afe

Transactions (1)

Coinbasef7a480df7d3554…a68d9a146a1afe

1 in → 1 out10.3800 XPM109 B

AH4jbUNY…Q397R4Rb

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.

1.547 × 10⁹⁷(98-digit number)

15470587375888877182…10186455637298613500

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

1.547 × 10⁹⁷(98-digit number)

15470587375888877182…10186455637298613499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.547 × 10⁹⁷(98-digit number)

15470587375888877182…10186455637298613501

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

3.094 × 10⁹⁷(98-digit number)

30941174751777754365…20372911274597226999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.094 × 10⁹⁷(98-digit number)

30941174751777754365…20372911274597227001

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

6.188 × 10⁹⁷(98-digit number)

61882349503555508730…40745822549194453999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.188 × 10⁹⁷(98-digit number)

61882349503555508730…40745822549194454001

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

1.237 × 10⁹⁸(99-digit number)

12376469900711101746…81491645098388907999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.237 × 10⁹⁸(99-digit number)

12376469900711101746…81491645098388908001

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

2.475 × 10⁹⁸(99-digit number)

24752939801422203492…62983290196777815999

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 135380

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 5865b7bb7f9761b04053094ce382d060c43ef7a57e3b43caeee573392a66a2a2

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 #135,380 on Chainz ↗