Home/Chain Registry/Block #97,190

Block #97,190

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/4/2013, 2:21:59 PM · Difficulty 9.2967 · 6,698,989 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

044aaf5af095b76e81dc52f39d9e371e8fcd9f7cfbf831e737577a5d606e3c7d

View on Chainz ↗

Height

#97,190

Difficulty

9.296660

Transactions

Size

205 B

Version

Bits

094bf1e2

Nonce

40,510

Timestamp

8/4/2013, 2:21:59 PM

Confirmations

6,698,989

Merkle Root

485e8e8598370b84f7ff40e821806cc7f6ecab5c6d54715a5e5ec8ca9e96cbe4

Transactions (1)

Coinbase485e8e8598370b…5ec8ca9e96cbe4

1 in → 1 out11.5500 XPM109 B

Acq3h2i5…PidcVmT6

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.

6.319 × 10¹⁰⁹(110-digit number)

63195906813548395125…71535776211468377940

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

6.319 × 10¹⁰⁹(110-digit number)

63195906813548395125…71535776211468377939

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.319 × 10¹⁰⁹(110-digit number)

63195906813548395125…71535776211468377941

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

1.263 × 10¹¹⁰(111-digit number)

12639181362709679025…43071552422936755879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.263 × 10¹¹⁰(111-digit number)

12639181362709679025…43071552422936755881

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

2.527 × 10¹¹⁰(111-digit number)

25278362725419358050…86143104845873511759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.527 × 10¹¹⁰(111-digit number)

25278362725419358050…86143104845873511761

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

5.055 × 10¹¹⁰(111-digit number)

50556725450838716100…72286209691747023519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.055 × 10¹¹⁰(111-digit number)

50556725450838716100…72286209691747023521

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

1.011 × 10¹¹¹(112-digit number)

10111345090167743220…44572419383494047039

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 97190

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 044aaf5af095b76e81dc52f39d9e371e8fcd9f7cfbf831e737577a5d606e3c7d

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 #97,190 on Chainz ↗