Home/Chain Registry/Block #62,649

Block #62,649

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 8:40:33 PM · Difficulty 8.9770 · 6,727,215 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a148f681f8dc6c89bf46b3e9fd270f5422e3c44bd17f5e7d6bedf7ca120288a

View on Chainz ↗

Height

#62,649

Difficulty

8.976965

Transactions

Size

207 B

Version

Bits

08fa1a60

Nonce

1,020

Timestamp

7/18/2013, 8:40:33 PM

Confirmations

6,727,215

Merkle Root

7b8e3e6c43648e938d4f8fc72ed27e9e926595dbf395eaa5d0ccd841ebcb8b3e

Transactions (1)

Coinbase7b8e3e6c43648e…ccd841ebcb8b3e

1 in → 1 out12.3900 XPM110 B

AP6yS8E7…UXmr3sAJ

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.

4.300 × 10¹¹⁰(111-digit number)

43007436327247127574…47904193346803502100

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

4.300 × 10¹¹⁰(111-digit number)

43007436327247127574…47904193346803502099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.300 × 10¹¹⁰(111-digit number)

43007436327247127574…47904193346803502101

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

8.601 × 10¹¹⁰(111-digit number)

86014872654494255149…95808386693607004199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.601 × 10¹¹⁰(111-digit number)

86014872654494255149…95808386693607004201

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

1.720 × 10¹¹¹(112-digit number)

17202974530898851029…91616773387214008399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.720 × 10¹¹¹(112-digit number)

17202974530898851029…91616773387214008401

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

3.440 × 10¹¹¹(112-digit number)

34405949061797702059…83233546774428016799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.440 × 10¹¹¹(112-digit number)

34405949061797702059…83233546774428016801

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

6.881 × 10¹¹¹(112-digit number)

68811898123595404119…66467093548856033599

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 62649

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 8a148f681f8dc6c89bf46b3e9fd270f5422e3c44bd17f5e7d6bedf7ca120288a

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 #62,649 on Chainz ↗