Block #138,408

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/28/2013, 9:36:25 AM · Difficulty 9.8261 · 6,652,963 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fc1bd05785acdd484dfea29e00ba73c8ea51c52cf3a3be51b407359b0b7967a1

View on Chainz ↗

Height

#138,408

Difficulty

9.826070

Transactions

Size

201 B

Version

Bits

09d3794d

Nonce

35,726

Timestamp

8/28/2013, 9:36:25 AM

Confirmations

6,652,963

Merkle Root

96da68b2fc141270f83e9ee3ba853a3d584f855f12b0e1ca3c3b150ba7346260

Transactions (1)

Coinbase96da68b2fc1412…3b150ba7346260

1 in → 1 out10.3400 XPM109 B

AVB3GBxS…ux3ibfyg

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.

2.036 × 10⁹⁸(99-digit number)

20362848934886898906…97108474601573217919

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

2.036 × 10⁹⁸(99-digit number)

20362848934886898906…97108474601573217919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.036 × 10⁹⁸(99-digit number)

20362848934886898906…97108474601573217921

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

4.072 × 10⁹⁸(99-digit number)

40725697869773797812…94216949203146435839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.072 × 10⁹⁸(99-digit number)

40725697869773797812…94216949203146435841

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

8.145 × 10⁹⁸(99-digit number)

81451395739547595624…88433898406292871679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.145 × 10⁹⁸(99-digit number)

81451395739547595624…88433898406292871681

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

1.629 × 10⁹⁹(100-digit number)

16290279147909519124…76867796812585743359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.629 × 10⁹⁹(100-digit number)

16290279147909519124…76867796812585743361

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

3.258 × 10⁹⁹(100-digit number)

32580558295819038249…53735593625171486719

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