Block #140,064

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/29/2013, 10:17:07 AM · Difficulty 9.8321 · 6,650,997 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

6,650,997

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…33052432950422616319

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.

★☆☆☆☆

Rarity

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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

Cross-reference on Chainz Explorer