Block #452,011

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/20/2014, 8:00:51 AM · Difficulty 10.3837 · 6,361,893 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6ad7553b9b3acaa464eda3a92124ab49a867040a2b4410090b2c8f88b806f718

View on Chainz ↗

Height

#452,011

Difficulty

10.383672

Transactions

Size

868 B

Version

Bits

0a62385c

Nonce

181,239

Timestamp

3/20/2014, 8:00:51 AM

Confirmations

6,361,893

Mined by

AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

70e95978c7911251f8db70819e316cc36bd21ae39a656ba0c59b462f17e87ed3

Transactions (1)

Coinbase70e95978c79112…9b462f17e87ed3

1 in → 21 out9.2600 XPM777 B

AdFLJFhb…bsaVkAyh AGz9gyZW…bo8NYQpw AcgDwGo8…BBFwbjVo Adbb4svj…dQWTHsq5 AMW1p9oT…2TzdaZxH

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.

1.734 × 10⁹⁶(97-digit number)

17343198861090728975…01036158562049151039

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

1.734 × 10⁹⁶(97-digit number)

17343198861090728975…01036158562049151039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.734 × 10⁹⁶(97-digit number)

17343198861090728975…01036158562049151041

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

3.468 × 10⁹⁶(97-digit number)

34686397722181457951…02072317124098302079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.468 × 10⁹⁶(97-digit number)

34686397722181457951…02072317124098302081

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

6.937 × 10⁹⁶(97-digit number)

69372795444362915903…04144634248196604159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.937 × 10⁹⁶(97-digit number)

69372795444362915903…04144634248196604161

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

1.387 × 10⁹⁷(98-digit number)

13874559088872583180…08289268496393208319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.387 × 10⁹⁷(98-digit number)

13874559088872583180…08289268496393208321

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

2.774 × 10⁹⁷(98-digit number)

27749118177745166361…16578536992786416639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.774 × 10⁹⁷(98-digit number)

27749118177745166361…16578536992786416641

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 #452,011

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