Block #423,303

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 9:13:34 AM · Difficulty 10.3702 · 6,394,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e4fea726c3332af490342f67f7966d425cfb03576cf463f6f958475677260b13

View on Chainz ↗

Height

#423,303

Difficulty

10.370234

Transactions

Size

868 B

Version

Bits

0a5ec7ab

Nonce

416,981

Timestamp

2/28/2014, 9:13:34 AM

Confirmations

6,394,515

Mined by

⛏️ uhAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

1ffd7f00e2a03e98abd8cd063b6b2b3f94c0a13500129e58d92b2a604ba5b04a

Transactions (1)

Coinbase1ffd7f00e2a03e…2b2a604ba5b04a

1 in → 21 out9.2800 XPM777 B

AdFLJFhb…bsaVkAyh AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx AUzEPJFG…kYkA5U9V AcgDwGo8…BBFwbjVo

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.

8.112 × 10⁹⁶(97-digit number)

81121526258615222112…25008096012702668799

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

8.112 × 10⁹⁶(97-digit number)

81121526258615222112…25008096012702668799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.112 × 10⁹⁶(97-digit number)

81121526258615222112…25008096012702668801

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

1.622 × 10⁹⁷(98-digit number)

16224305251723044422…50016192025405337599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.622 × 10⁹⁷(98-digit number)

16224305251723044422…50016192025405337601

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

3.244 × 10⁹⁷(98-digit number)

32448610503446088844…00032384050810675199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.244 × 10⁹⁷(98-digit number)

32448610503446088844…00032384050810675201

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

6.489 × 10⁹⁷(98-digit number)

64897221006892177689…00064768101621350399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.489 × 10⁹⁷(98-digit number)

64897221006892177689…00064768101621350401

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

1.297 × 10⁹⁸(99-digit number)

12979444201378435537…00129536203242700799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.297 × 10⁹⁸(99-digit number)

12979444201378435537…00129536203242700801

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 #423,303

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