Block #465,626

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/29/2014, 2:13:01 PM · Difficulty 10.4259 · 6,345,482 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

144b21fc1e59c92f6a60201b1f57639a33802adeaa6625649a48b27f0d3d02bd

View on Chainz ↗

Height

#465,626

Difficulty

10.425946

Transactions

Size

1.87 KB

Version

Bits

0a6d0aca

Nonce

306,311

Timestamp

3/29/2014, 2:13:01 PM

Confirmations

6,345,482

Mined by

⛏️ YxxAGz9gyZWgxBxAyVrKrWDzMw21kbo8NYQpw

Merkle Root

ead7e7a96c07a35ea1cbe84d503c956382b6f83d87c66fd5c801fd55155d7480

Transactions (5)

Coinbase8c6d50fbfcd988…021d638c4a2d65

1 in → 22 out9.2300 XPM811 B

AGz9gyZW…bo8NYQpw AdFLJFhb…bsaVkAyh AbPcCMg4…719q6mAX AMW1p9oT…2TzdaZxH ATp4jJhs…TbSgR8Qb

385ac23d476ebf…144de3f9c741ae

1 in → 2 out9.1900 XPM226 B

APGeMpJd…pX2gQVyW Ac24WwPt…BSeTbxUj

ceacbf123d7e22…7791b2b201b1f3

2 in → 1 out4.5449 XPM338 B

AQm7AQJF…Vb2i2NkG

eeae40f669e8e1…539f6991224b00

1 in → 2 out6.9900 XPM227 B

Ae8ZExg5…tAZdwMQE Abn6y2Gn…vu7zM25p

c168d5ee0b61b4…3b65f5eb4ce5e8

1 in → 2 out2.0800 XPM225 B

AYBzzCHX…nDnB1bQ9 Ae8ZExg5…tAZdwMQE

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.

4.314 × 10⁹⁵(96-digit number)

43147426923626871413…10391812392817196379

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

4.314 × 10⁹⁵(96-digit number)

43147426923626871413…10391812392817196379

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.314 × 10⁹⁵(96-digit number)

43147426923626871413…10391812392817196381

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

8.629 × 10⁹⁵(96-digit number)

86294853847253742827…20783624785634392759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.629 × 10⁹⁵(96-digit number)

86294853847253742827…20783624785634392761

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

1.725 × 10⁹⁶(97-digit number)

17258970769450748565…41567249571268785519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.725 × 10⁹⁶(97-digit number)

17258970769450748565…41567249571268785521

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

3.451 × 10⁹⁶(97-digit number)

34517941538901497130…83134499142537571039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.451 × 10⁹⁶(97-digit number)

34517941538901497130…83134499142537571041

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

6.903 × 10⁹⁶(97-digit number)

69035883077802994261…66268998285075142079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.903 × 10⁹⁶(97-digit number)

69035883077802994261…66268998285075142081

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 #465,626

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