Home/Chain Registry/Block #230,760

Block #230,760

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/28/2013, 12:33:01 AM · Difficulty 9.9399 · 6,561,853 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

626f68b2a8a17cf647351f4936b616af29c82213b3c9f7689cec987234daedcb

View on Chainz ↗

Height

#230,760

Difficulty

9.939851

Transactions

Size

213 B

Version

Bits

09f09a15

Nonce

16,808,922

Timestamp

10/28/2013, 12:33:01 AM

Confirmations

6,561,853

Merkle Root

4bbb59ec53c737013b33ac1779091b2d62db3d8170c91f075b47dd6f46a437a1

Transactions (1)

Coinbase4bbb59ec53c737…47dd6f46a437a1

1 in → 1 out10.1100 XPM118 B

ARg8Kp4c…n7AUWZXy

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.

3.336 × 10¹⁰⁵(106-digit number)

33360293841708042999…44060619171419914240

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

3.336 × 10¹⁰⁵(106-digit number)

33360293841708042999…44060619171419914239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.336 × 10¹⁰⁵(106-digit number)

33360293841708042999…44060619171419914241

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

6.672 × 10¹⁰⁵(106-digit number)

66720587683416085998…88121238342839828479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.672 × 10¹⁰⁵(106-digit number)

66720587683416085998…88121238342839828481

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

1.334 × 10¹⁰⁶(107-digit number)

13344117536683217199…76242476685679656959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.334 × 10¹⁰⁶(107-digit number)

13344117536683217199…76242476685679656961

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

2.668 × 10¹⁰⁶(107-digit number)

26688235073366434399…52484953371359313919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.668 × 10¹⁰⁶(107-digit number)

26688235073366434399…52484953371359313921

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

5.337 × 10¹⁰⁶(107-digit number)

53376470146732868798…04969906742718627839

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 230760

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 626f68b2a8a17cf647351f4936b616af29c82213b3c9f7689cec987234daedcb

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 #230,760 on Chainz ↗