Block #134,611

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/26/2013, 3:39:48 AM · Difficulty 9.8055 · 6,675,624 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16dc7659e739a1b35a662c36bbd8da2cd71dcad152a674a5b136838afe899e80

View on Chainz ↗

Height

#134,611

Difficulty

9.805473

Transactions

Size

1022 B

Version

Bits

09ce3381

Nonce

28,582

Timestamp

8/26/2013, 3:39:48 AM

Confirmations

6,675,624

Mined by

⛏️ P2SHAKv2pG2XeqFCFtpxnVA9FFBF45nx52k8U6

Merkle Root

49b3f19b85f77a10a4265569f80d7e4ef78cd70be8b38309c8579e1c47b849ac

Transactions (2)

Coinbase3bca45d6e97a79…82b22366464d19

1 in → 1 out10.4000 XPM109 B

AKv2pG2X…nx52k8U6

8ca9609fd8510d…8fd32c44f5db5f

5 in → 2 out55.5873 XPM820 B

AKMsdd8i…ZxE6Md7T ATaoKCT8…XEibRZ1T

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.

5.525 × 10¹⁰²(103-digit number)

55253237403617487454…23380960930944999659

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

5.525 × 10¹⁰²(103-digit number)

55253237403617487454…23380960930944999659

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.525 × 10¹⁰²(103-digit number)

55253237403617487454…23380960930944999661

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

1.105 × 10¹⁰³(104-digit number)

11050647480723497490…46761921861889999319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.105 × 10¹⁰³(104-digit number)

11050647480723497490…46761921861889999321

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

2.210 × 10¹⁰³(104-digit number)

22101294961446994981…93523843723779998639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.210 × 10¹⁰³(104-digit number)

22101294961446994981…93523843723779998641

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

4.420 × 10¹⁰³(104-digit number)

44202589922893989963…87047687447559997279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.420 × 10¹⁰³(104-digit number)

44202589922893989963…87047687447559997281

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

8.840 × 10¹⁰³(104-digit number)

88405179845787979926…74095374895119994559

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

Block #134,611

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