Home/Chain Registry/Block #121,689

Block #121,689

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/17/2013, 11:40:26 PM · Difficulty 9.7545 · 6,705,297 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b6c76755c701c802ae453154499634d17cef51bbc03aee4e47b738ee8683e05a

View on Chainz ↗

Height

#121,689

Difficulty

9.754519

Transactions

Size

584 B

Version

Bits

09c12824

Nonce

626,258

Timestamp

8/17/2013, 11:40:26 PM

Confirmations

6,705,297

Merkle Root

0f97421c0bd01ea684e391e3c17191553e551f32a9b525e0c0c465b3427380ef

Transactions (3)

Coinbase799921b0d199a0…879b375e62a19b

1 in → 1 out10.5100 XPM109 B

AGXS5BR4…WtNUVc3H

b0f8a29a7be14e…15d58bdefeb504

1 in → 2 out10.5100 XPM191 B

AYoLWyLb…6twgbK8X AaMRUFMG…S11BNFrC

1540a906609d16…cd6def6833200c

1 in → 1 out5.2500 XPM192 B

AeguK5Ai…CLUqoF9q

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.

4.904 × 10⁹⁹(100-digit number)

49040695622913114026…06412439320378617080

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

4.904 × 10⁹⁹(100-digit number)

49040695622913114026…06412439320378617079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.904 × 10⁹⁹(100-digit number)

49040695622913114026…06412439320378617081

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

9.808 × 10⁹⁹(100-digit number)

98081391245826228052…12824878640757234159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.808 × 10⁹⁹(100-digit number)

98081391245826228052…12824878640757234161

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

1.961 × 10¹⁰⁰(101-digit number)

19616278249165245610…25649757281514468319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.961 × 10¹⁰⁰(101-digit number)

19616278249165245610…25649757281514468321

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

3.923 × 10¹⁰⁰(101-digit number)

39232556498330491221…51299514563028936639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.923 × 10¹⁰⁰(101-digit number)

39232556498330491221…51299514563028936641

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

7.846 × 10¹⁰⁰(101-digit number)

78465112996660982442…02599029126057873279

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 121689

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 b6c76755c701c802ae453154499634d17cef51bbc03aee4e47b738ee8683e05a

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 #121,689 on Chainz ↗

Block #121,689

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