Home/Chain Registry/Block #35,800

Block #35,800

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/14/2013, 8:35:24 AM · Difficulty 7.9948 · 6,754,247 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c5e96dad1c3af27bfe32fd7f8247b948fddea7a162c1d280d519cedacf7234f5

View on Chainz ↗

Height

#35,800

Difficulty

7.994783

Transactions

Size

198 B

Version

Bits

07feaa13

Nonce

208

Timestamp

7/14/2013, 8:35:24 AM

Confirmations

6,754,247

Merkle Root

f345d62dbfd3df9073414503c8390f5903138785bff34d7c105385c38714a002

Transactions (1)

Coinbasef345d62dbfd3df…5385c38714a002

1 in → 1 out15.6200 XPM109 B

ALsDsAZM…EV8LNs7T

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.

8.071 × 10⁹¹(92-digit number)

80712310362577304179…64789215074477608160

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

8.071 × 10⁹¹(92-digit number)

80712310362577304179…64789215074477608159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.071 × 10⁹¹(92-digit number)

80712310362577304179…64789215074477608161

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

1.614 × 10⁹²(93-digit number)

16142462072515460835…29578430148955216319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.614 × 10⁹²(93-digit number)

16142462072515460835…29578430148955216321

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

3.228 × 10⁹²(93-digit number)

32284924145030921671…59156860297910432639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.228 × 10⁹²(93-digit number)

32284924145030921671…59156860297910432641

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

6.456 × 10⁹²(93-digit number)

64569848290061843343…18313720595820865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.456 × 10⁹²(93-digit number)

64569848290061843343…18313720595820865281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 35800

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 c5e96dad1c3af27bfe32fd7f8247b948fddea7a162c1d280d519cedacf7234f5

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 #35,800 on Chainz ↗