Home/Chain Registry/Block #140,064

Block #140,064

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/29/2013, 10:17:07 AM · Difficulty 9.8321 · 6,649,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f101d0e6ee97fc7579f60267e0a13c3c0cbc9bd647c4a7b61aa7c72e3835b212

View on Chainz ↗

Height

#140,064

Difficulty

9.832139

Transactions

Size

200 B

Version

Bits

09d5070f

Nonce

244,812

Timestamp

8/29/2013, 10:17:07 AM

Confirmations

6,649,760

Merkle Root

ae774a08a9ad309fe58016a9bd9b367e076e79f4c413026ce5669cd23ff68032

Transactions (1)

Coinbaseae774a08a9ad30…669cd23ff68032

1 in → 1 out10.3300 XPM109 B

AGQxUjMH…N57UCU7n

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.

1.975 × 10⁹⁶(97-digit number)

19758441461878833335…33052432950422616320

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

1.975 × 10⁹⁶(97-digit number)

19758441461878833335…33052432950422616319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.975 × 10⁹⁶(97-digit number)

19758441461878833335…33052432950422616321

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

3.951 × 10⁹⁶(97-digit number)

39516882923757666670…66104865900845232639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.951 × 10⁹⁶(97-digit number)

39516882923757666670…66104865900845232641

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

7.903 × 10⁹⁶(97-digit number)

79033765847515333341…32209731801690465279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.903 × 10⁹⁶(97-digit number)

79033765847515333341…32209731801690465281

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

1.580 × 10⁹⁷(98-digit number)

15806753169503066668…64419463603380930559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.580 × 10⁹⁷(98-digit number)

15806753169503066668…64419463603380930561

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

3.161 × 10⁹⁷(98-digit number)

31613506339006133336…28838927206761861119

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 140064

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 f101d0e6ee97fc7579f60267e0a13c3c0cbc9bd647c4a7b61aa7c72e3835b212

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 #140,064 on Chainz ↗