Block #423,603

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 1:21:16 PM · Difficulty 10.3767 · 6,384,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

05e1dc5c806716c33f012278d18be1e5274c48b7b70af5017c5ea6cd4e006675

View on Chainz ↗

Height

#423,603

Difficulty

10.376676

Transactions

Size

866 B

Version

Bits

0a606dd6

Nonce

30,898

Timestamp

2/28/2014, 1:21:16 PM

Confirmations

6,384,643

Mined by

⛏️ vaSAAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

f5d14fe27f1341617f0cbf882df7e2f26cb9c0460f058f993a23fd5dee104474

Transactions (1)

Coinbasef5d14fe27f1341…23fd5dee104474

1 in → 21 out9.2700 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 ATKK7iFz…wZm46KN1 AGKhfQo2…h7fBXLX6 ARSeozDw…C9HtARnj

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.

1.385 × 10⁹¹(92-digit number)

13858126347412144714…47159541351022373239

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

1.385 × 10⁹¹(92-digit number)

13858126347412144714…47159541351022373239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.385 × 10⁹¹(92-digit number)

13858126347412144714…47159541351022373241

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

2.771 × 10⁹¹(92-digit number)

27716252694824289428…94319082702044746479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.771 × 10⁹¹(92-digit number)

27716252694824289428…94319082702044746481

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

5.543 × 10⁹¹(92-digit number)

55432505389648578857…88638165404089492959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.543 × 10⁹¹(92-digit number)

55432505389648578857…88638165404089492961

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

1.108 × 10⁹²(93-digit number)

11086501077929715771…77276330808178985919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.108 × 10⁹²(93-digit number)

11086501077929715771…77276330808178985921

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

2.217 × 10⁹²(93-digit number)

22173002155859431543…54552661616357971839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.217 × 10⁹²(93-digit number)

22173002155859431543…54552661616357971841

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

Block #423,603

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