Block #435,540

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/9/2014, 12:23:45 AM · Difficulty 10.3518 · 6,381,204 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

59849760d8d0c4d81ec33290a63b964abacab17ef9ea5e197d6cae3634954fab

View on Chainz ↗

Height

#435,540

Difficulty

10.351758

Transactions

Size

52.05 KB

Version

Bits

0a5a0cca

Nonce

151,693

Timestamp

3/9/2014, 12:23:45 AM

Confirmations

6,381,204

Mined by

⛏️ Th5AdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

38c79d8d3ab38e9dd53a8b871d50724fe245f44c6cb0f2bc0a0966fc279fcdde

Transactions (3)

Coinbasef4e8511e123f93…038d34e9b319cf

1 in → 24 out9.8600 XPM879 B

AdFLJFhb…bsaVkAyh AVRMvm7T…6PC6keBx AcuM7XiJ…5uND8Jce AZqjMFvv…G8aw2zC8 ASgUri65…C7NLcyBg

45845103c8e97f…1f064ac6a064d0

1 in → 1 out9.3400 XPM158 B

ARA9Q1ay…t4EzMknt

314c992df5669d…bfdc274070550b

352 in → 2 out500.0921 XPM50.95 KB

AUHiF4Xn…PgMqrrYD AJjnK9uC…VreFquR4

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.

4.239 × 10⁹⁴(95-digit number)

42399377110432704226…06643778076023623759

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

4.239 × 10⁹⁴(95-digit number)

42399377110432704226…06643778076023623759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.239 × 10⁹⁴(95-digit number)

42399377110432704226…06643778076023623761

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

8.479 × 10⁹⁴(95-digit number)

84798754220865408453…13287556152047247519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.479 × 10⁹⁴(95-digit number)

84798754220865408453…13287556152047247521

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

1.695 × 10⁹⁵(96-digit number)

16959750844173081690…26575112304094495039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.695 × 10⁹⁵(96-digit number)

16959750844173081690…26575112304094495041

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

3.391 × 10⁹⁵(96-digit number)

33919501688346163381…53150224608188990079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.391 × 10⁹⁵(96-digit number)

33919501688346163381…53150224608188990081

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

6.783 × 10⁹⁵(96-digit number)

67839003376692326763…06300449216377980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.783 × 10⁹⁵(96-digit number)

67839003376692326763…06300449216377980161

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 #435,540

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