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Block #30,898

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/13/2013, 9:08:22 PM · Difficulty 7.9877 · 6,786,480 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74aea161fbb4e8edb2a4d54547d7fa0671748e7d7c834980957b02d8cca0bd5d

View on Chainz ↗

Height

#30,898

Difficulty

7.987734

Transactions

Size

201 B

Version

Bits

07fcdc24

Nonce

Timestamp

7/13/2013, 9:08:22 PM

Confirmations

6,786,480

Merkle Root

3e8f328a4382b4b97b3987508f1338ae2e4af32eaa247b23ff950973f1f1fd67

Transactions (1)

Coinbase3e8f328a4382b4…950973f1f1fd67

1 in → 1 out15.6500 XPM108 B

ASbRxSSz…H5rkdjdH

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.

1.121 × 10¹⁰³(104-digit number)

11210150072851930542…16092477421905761840

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

1.121 × 10¹⁰³(104-digit number)

11210150072851930542…16092477421905761839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.121 × 10¹⁰³(104-digit number)

11210150072851930542…16092477421905761841

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

2.242 × 10¹⁰³(104-digit number)

22420300145703861084…32184954843811523679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.242 × 10¹⁰³(104-digit number)

22420300145703861084…32184954843811523681

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

4.484 × 10¹⁰³(104-digit number)

44840600291407722169…64369909687623047359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.484 × 10¹⁰³(104-digit number)

44840600291407722169…64369909687623047361

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

8.968 × 10¹⁰³(104-digit number)

89681200582815444339…28739819375246094719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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 30898

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 74aea161fbb4e8edb2a4d54547d7fa0671748e7d7c834980957b02d8cca0bd5d

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 #30,898 on Chainz ↗

Block #30,898

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