Home/Chain Registry/Block #215,658

Block #215,658

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/18/2013, 6:00:47 AM · Difficulty 9.9254 · 6,577,637 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4302ac174bafb375e1c05193c329ed52bbb3953e4ae318d4ab77b470d06957e8

View on Chainz ↗

Height

#215,658

Difficulty

9.925365

Transactions

Size

206 B

Version

Bits

09ece4ba

Nonce

67,108,935

Timestamp

10/18/2013, 6:00:47 AM

Confirmations

6,577,637

Merkle Root

bd5a894461684de70360f2442bba0f86a655f0b2ba0897a01c70e2a2558cf471

Transactions (1)

Coinbasebd5a894461684d…70e2a2558cf471

1 in → 1 out10.1400 XPM116 B

AcLBm5Z9…S683d7c3

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.

6.138 × 10⁹³(94-digit number)

61386870380109734750…80051108270779611000

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

6.138 × 10⁹³(94-digit number)

61386870380109734750…80051108270779610999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.138 × 10⁹³(94-digit number)

61386870380109734750…80051108270779611001

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

1.227 × 10⁹⁴(95-digit number)

12277374076021946950…60102216541559221999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.227 × 10⁹⁴(95-digit number)

12277374076021946950…60102216541559222001

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

2.455 × 10⁹⁴(95-digit number)

24554748152043893900…20204433083118443999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.455 × 10⁹⁴(95-digit number)

24554748152043893900…20204433083118444001

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

4.910 × 10⁹⁴(95-digit number)

49109496304087787800…40408866166236887999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.910 × 10⁹⁴(95-digit number)

49109496304087787800…40408866166236888001

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

9.821 × 10⁹⁴(95-digit number)

98218992608175575601…80817732332473775999

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 215658

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 4302ac174bafb375e1c05193c329ed52bbb3953e4ae318d4ab77b470d06957e8

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 #215,658 on Chainz ↗