Home/Chain Registry/Block #62,218

Block #62,218

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/18/2013, 5:50:19 PM · Difficulty 8.9757 · 6,729,958 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b42bc3cce236ad5309c2ee0221ec7da04a7bc30bc058d5ebcc34803e23226a32

View on Chainz ↗

Height

#62,218

Difficulty

8.975729

Transactions

Size

361 B

Version

Bits

08f9c95d

Nonce

791

Timestamp

7/18/2013, 5:50:19 PM

Confirmations

6,729,958

Merkle Root

561dceb9a5f02f4b92883cefcea9f9f7609b412249702846d7ff4f100e942aa0

Transactions (2)

Coinbase1901f5e1d7abeb…51c1889b91da76

1 in → 1 out12.4100 XPM110 B

AW6sZe1N…2KCe8gN3

81d7d3bb39c8d5…c74bd16c221b8f

1 in → 1 out13.1100 XPM159 B

ANevLLRs…a2Ed88k4

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.

1.465 × 10¹⁰⁰(101-digit number)

14659798458123532560…90929380647533607830

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

1.465 × 10¹⁰⁰(101-digit number)

14659798458123532560…90929380647533607829

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.465 × 10¹⁰⁰(101-digit number)

14659798458123532560…90929380647533607831

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

2.931 × 10¹⁰⁰(101-digit number)

29319596916247065120…81858761295067215659

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.931 × 10¹⁰⁰(101-digit number)

29319596916247065120…81858761295067215661

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

5.863 × 10¹⁰⁰(101-digit number)

58639193832494130241…63717522590134431319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.863 × 10¹⁰⁰(101-digit number)

58639193832494130241…63717522590134431321

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

1.172 × 10¹⁰¹(102-digit number)

11727838766498826048…27435045180268862639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.172 × 10¹⁰¹(102-digit number)

11727838766498826048…27435045180268862641

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

2.345 × 10¹⁰¹(102-digit number)

23455677532997652096…54870090360537725279

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 62218

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 b42bc3cce236ad5309c2ee0221ec7da04a7bc30bc058d5ebcc34803e23226a32

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 #62,218 on Chainz ↗