Block #168,383

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/17/2013, 6:30:23 AM · Difficulty 9.8684 · 6,642,115 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

78a60c00000c3b96e7b75bbde8ec9a5d3caea9852b363d758e1c4f258ce222a6

View on Chainz ↗

Height

#168,383

Difficulty

9.868449

Transactions

Size

426 B

Version

Bits

09de52a7

Nonce

62,951

Timestamp

9/17/2013, 6:30:23 AM

Confirmations

6,642,115

Mined by

⛏️ P2SHATt3BjbGkb311s5127UZUQYQ2ywtyrbLAb

Merkle Root

e9275122fa18d329a93d5c688deb63424e74ec7f8a13c08035a1fac528cb1b35

Transactions (2)

Coinbasee75eb8a3ce04ec…cd0dcd1477b2ab

1 in → 1 out10.2600 XPM109 B

ATt3BjbG…wtyrbLAb

bdf3e12c7557f8…b46cf8950c80a9

1 in → 2 out3.0735 XPM226 B

AeVbwwQu…1CKd9JmB AFwX4Qx4…4XPVekk1

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.

1.400 × 10⁹⁶(97-digit number)

14007509520847170374…48837104110344847359

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

1.400 × 10⁹⁶(97-digit number)

14007509520847170374…48837104110344847359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.400 × 10⁹⁶(97-digit number)

14007509520847170374…48837104110344847361

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

2.801 × 10⁹⁶(97-digit number)

28015019041694340749…97674208220689694719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.801 × 10⁹⁶(97-digit number)

28015019041694340749…97674208220689694721

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

5.603 × 10⁹⁶(97-digit number)

56030038083388681498…95348416441379389439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.603 × 10⁹⁶(97-digit number)

56030038083388681498…95348416441379389441

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

1.120 × 10⁹⁷(98-digit number)

11206007616677736299…90696832882758778879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.120 × 10⁹⁷(98-digit number)

11206007616677736299…90696832882758778881

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

2.241 × 10⁹⁷(98-digit number)

22412015233355472599…81393665765517557759

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 #168,383

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