Home/Chain Registry/Block #90,143

Block #90,143

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 9:24:34 PM · Difficulty 9.2527 · 6,707,821 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3b9c769bf8b73a51c80864a47a8c2c66332d7646a721f2c1501fe9495b624fd8

View on Chainz ↗

Height

#90,143

Difficulty

9.252731

Transactions

Size

208 B

Version

Bits

0940b2fb

Nonce

23,596

Timestamp

7/30/2013, 9:24:34 PM

Confirmations

6,707,821

Merkle Root

59d291c2c777a3de2f5ea7ea50076b505c7577fd8a6a9bf9c0c9c0056999b1ff

Transactions (1)

Coinbase59d291c2c777a3…c9c0056999b1ff

1 in → 1 out11.6600 XPM109 B

AM8siW8U…DREaAJi5

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.

3.552 × 10¹¹⁶(117-digit number)

35523953919588571453…78859043843817848510

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

3.552 × 10¹¹⁶(117-digit number)

35523953919588571453…78859043843817848509

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.552 × 10¹¹⁶(117-digit number)

35523953919588571453…78859043843817848511

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

7.104 × 10¹¹⁶(117-digit number)

71047907839177142907…57718087687635697019

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.104 × 10¹¹⁶(117-digit number)

71047907839177142907…57718087687635697021

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

1.420 × 10¹¹⁷(118-digit number)

14209581567835428581…15436175375271394039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.420 × 10¹¹⁷(118-digit number)

14209581567835428581…15436175375271394041

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

2.841 × 10¹¹⁷(118-digit number)

28419163135670857162…30872350750542788079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.841 × 10¹¹⁷(118-digit number)

28419163135670857162…30872350750542788081

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

5.683 × 10¹¹⁷(118-digit number)

56838326271341714325…61744701501085576159

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 90143

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 3b9c769bf8b73a51c80864a47a8c2c66332d7646a721f2c1501fe9495b624fd8

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 #90,143 on Chainz ↗