Home/Chain Registry/Block #200,395

Block #200,395

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 11:48:42 PM · Difficulty 9.8894 · 6,600,693 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

800832f3020ea9d7b3b089a3b7b7ff977cfeb533d914d00b7cbdecf4a4940f73

View on Chainz ↗

Height

#200,395

Difficulty

9.889435

Transactions

Size

423 B

Version

Bits

09e3b201

Nonce

26,495

Timestamp

10/8/2013, 11:48:42 PM

Confirmations

6,600,693

Merkle Root

bf7580f7e9d897d9a191651390a8492b8cd3b2aa367ad4e05acdc47ac1dd2b95

Transactions (2)

Coinbaseecd55a4a5d2a70…6d99fc8986ed86

1 in → 1 out10.2200 XPM109 B

AcGNiyYT…XwvxdZTe

e608c36be13c2a…007e19abbab0d3

1 in → 2 out24.8900 XPM225 B

ASUJFtQT…Cqr8nBVx AVsAwdUG…J45CG7Rv

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.

1.188 × 10⁹²(93-digit number)

11887959946580871074…56709712512521752780

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

1.188 × 10⁹²(93-digit number)

11887959946580871074…56709712512521752779

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.188 × 10⁹²(93-digit number)

11887959946580871074…56709712512521752781

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

2.377 × 10⁹²(93-digit number)

23775919893161742149…13419425025043505559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.377 × 10⁹²(93-digit number)

23775919893161742149…13419425025043505561

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

4.755 × 10⁹²(93-digit number)

47551839786323484299…26838850050087011119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.755 × 10⁹²(93-digit number)

47551839786323484299…26838850050087011121

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

9.510 × 10⁹²(93-digit number)

95103679572646968599…53677700100174022239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.510 × 10⁹²(93-digit number)

95103679572646968599…53677700100174022241

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

1.902 × 10⁹³(94-digit number)

19020735914529393719…07355400200348044479

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 200395

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 800832f3020ea9d7b3b089a3b7b7ff977cfeb533d914d00b7cbdecf4a4940f73

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 #200,395 on Chainz ↗