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Block #66,414

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/19/2013, 5:19:14 PM · Difficulty 8.9861 · 6,723,631 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c84d0a165a9b04e3f36386e7ed7baaa4a02bd6efafb756a42e874d86b7beb5d

View on Chainz ↗

Height

#66,414

Difficulty

8.986138

Transactions

Size

206 B

Version

Bits

08fc7382

Nonce

167

Timestamp

7/19/2013, 5:19:14 PM

Confirmations

6,723,631

Merkle Root

6ddab1b94974da6fb6fababce8cc13a1aa4de11120e7196a4c923695379da02c

Transactions (1)

Coinbase6ddab1b94974da…923695379da02c

1 in → 1 out12.3700 XPM109 B

AJBcJaLo…ehmWaupr

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.

4.450 × 10¹¹¹(112-digit number)

44501338920485059931…64803675590755619570

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

4.450 × 10¹¹¹(112-digit number)

44501338920485059931…64803675590755619569

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.450 × 10¹¹¹(112-digit number)

44501338920485059931…64803675590755619571

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

8.900 × 10¹¹¹(112-digit number)

89002677840970119863…29607351181511239139

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.900 × 10¹¹¹(112-digit number)

89002677840970119863…29607351181511239141

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

1.780 × 10¹¹²(113-digit number)

17800535568194023972…59214702363022478279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.780 × 10¹¹²(113-digit number)

17800535568194023972…59214702363022478281

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

3.560 × 10¹¹²(113-digit number)

35601071136388047945…18429404726044956559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.560 × 10¹¹²(113-digit number)

35601071136388047945…18429404726044956561

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

7.120 × 10¹¹²(113-digit number)

71202142272776095890…36858809452089913119

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 66414

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 7c84d0a165a9b04e3f36386e7ed7baaa4a02bd6efafb756a42e874d86b7beb5d

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 #66,414 on Chainz ↗