Home/Chain Registry/Block #89,357

Block #89,357

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 7:29:51 AM · Difficulty 9.2600 · 6,707,059 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dda9a5b22d9383fcfa57c6677a7626827f03dc87ff35d7a500b49fb4e57cc7ec

View on Chainz ↗

Height

#89,357

Difficulty

9.259975

Transactions

Size

400 B

Version

Bits

09428dbe

Nonce

53,830

Timestamp

7/30/2013, 7:29:51 AM

Confirmations

6,707,059

Merkle Root

2bcb7fdfd808de81e789a7ec949ee0951126c161743e087e70c3bca93b8104e2

Transactions (2)

Coinbased0342ea464f9f1…1ee848e2949ea1

1 in → 1 out11.6600 XPM109 B

AeAHz6BX…V41YqTZc

26c76b2ea40e36…28fc6e607e29fa

1 in → 2 out11.5600 XPM191 B

AWurFxDY…o9PwGQjD ARgejNjo…FdnMQoh2

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.

4.582 × 10¹¹⁸(119-digit number)

45829003409630909193…57389349834614772000

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

4.582 × 10¹¹⁸(119-digit number)

45829003409630909193…57389349834614771999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.582 × 10¹¹⁸(119-digit number)

45829003409630909193…57389349834614772001

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

9.165 × 10¹¹⁸(119-digit number)

91658006819261818387…14778699669229543999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.165 × 10¹¹⁸(119-digit number)

91658006819261818387…14778699669229544001

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

1.833 × 10¹¹⁹(120-digit number)

18331601363852363677…29557399338459087999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.833 × 10¹¹⁹(120-digit number)

18331601363852363677…29557399338459088001

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

3.666 × 10¹¹⁹(120-digit number)

36663202727704727355…59114798676918175999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.666 × 10¹¹⁹(120-digit number)

36663202727704727355…59114798676918176001

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

7.332 × 10¹¹⁹(120-digit number)

73326405455409454710…18229597353836351999

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 89357

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 dda9a5b22d9383fcfa57c6677a7626827f03dc87ff35d7a500b49fb4e57cc7ec

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 #89,357 on Chainz ↗