Block #390,189

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2014, 11:49:57 PM · Difficulty 10.4245 · 6,406,329 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

887ca58b8a9104ae0545436e013705d3d6ac4194a3792c7ac1bcb702456f2196

View on Chainz ↗

Height

#390,189

Difficulty

10.424464

Transactions

Size

968 B

Version

Bits

0a6ca9b2

Nonce

153,761

Timestamp

2/4/2014, 11:49:57 PM

Confirmations

6,406,329

Mined by

⛏️ -aR|yAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

7260050f0dec36a0adb53df524f87b6ee94ce95fd547f4af669460fa5ca9ba91

Transactions (1)

Coinbase7260050f0dec36…9460fa5ca9ba91

1 in → 24 out9.1900 XPM879 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AGKhfQo2…h7fBXLX6 ALqxX1WA…hsKjbnXn ATKK7iFz…wZm46KN1

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.

1.314 × 10⁹²(93-digit number)

13146022457988709336…23802114267406017439

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

1.314 × 10⁹²(93-digit number)

13146022457988709336…23802114267406017439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.314 × 10⁹²(93-digit number)

13146022457988709336…23802114267406017441

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

2.629 × 10⁹²(93-digit number)

26292044915977418672…47604228534812034879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.629 × 10⁹²(93-digit number)

26292044915977418672…47604228534812034881

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

5.258 × 10⁹²(93-digit number)

52584089831954837344…95208457069624069759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.258 × 10⁹²(93-digit number)

52584089831954837344…95208457069624069761

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

1.051 × 10⁹³(94-digit number)

10516817966390967468…90416914139248139519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.051 × 10⁹³(94-digit number)

10516817966390967468…90416914139248139521

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

2.103 × 10⁹³(94-digit number)

21033635932781934937…80833828278496279039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.103 × 10⁹³(94-digit number)

21033635932781934937…80833828278496279041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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