Home/Chain Registry/Block #2,762,019

Block #2,762,019

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/23/2018, 7:30:08 PM · Difficulty 11.6543 · 4,071,034 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b9a3791dc66a01370aed27adcdf2dd5ba9bcdc83bed89d2c6c7263c02125ae99

View on Chainz ↗

Height

#2,762,019

Difficulty

11.654335

Transactions

Size

3.16 KB

Version

Bits

0ba7827a

Nonce

798,101,055

Timestamp

7/23/2018, 7:30:08 PM

Confirmations

4,071,034

Merkle Root

47b9819c19ca9d35b7a7f8669ff8a41c3a6d655035c51ec478d682043c8845d7

Transactions (2)

Coinbase6ffebc54fe2818…0e209a015d1842

1 in → 1 out7.3900 XPM110 B

AWTmRyrh…wc4WkSDi

a8184e219df871…fdddfa3046bc14

20 in → 2 out19160.4849 XPM2.97 KB

AYroy9Y9…ARnBPcoG AYwGcjiV…iEHMTxm4

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.

8.830 × 10⁹⁷(98-digit number)

88307019299239303663…51012155553130086400

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

8.830 × 10⁹⁷(98-digit number)

88307019299239303663…51012155553130086399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.830 × 10⁹⁷(98-digit number)

88307019299239303663…51012155553130086401

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

1.766 × 10⁹⁸(99-digit number)

17661403859847860732…02024311106260172799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.766 × 10⁹⁸(99-digit number)

17661403859847860732…02024311106260172801

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

3.532 × 10⁹⁸(99-digit number)

35322807719695721465…04048622212520345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.532 × 10⁹⁸(99-digit number)

35322807719695721465…04048622212520345601

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

7.064 × 10⁹⁸(99-digit number)

70645615439391442930…08097244425040691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.064 × 10⁹⁸(99-digit number)

70645615439391442930…08097244425040691201

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

1.412 × 10⁹⁹(100-digit number)

14129123087878288586…16194488850081382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.412 × 10⁹⁹(100-digit number)

14129123087878288586…16194488850081382401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.825 × 10⁹⁹(100-digit number)

28258246175756577172…32388977700162764799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

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 2762019

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 b9a3791dc66a01370aed27adcdf2dd5ba9bcdc83bed89d2c6c7263c02125ae99

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 #2,762,019 on Chainz ↗

Block #2,762,019

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