Block #276,458

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/27/2013, 4:57:40 AM · Difficulty 9.9632 · 6,533,691 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

976bc84423f80cc9f9c4c6493547838e545a86151b65ee09987442195c8f7d01

View on Chainz ↗

Height

#276,458

Difficulty

9.963217

Transactions

Size

2.87 KB

Version

Bits

09f69562

Nonce

97,604

Timestamp

11/27/2013, 4:57:40 AM

Confirmations

6,533,691

Mined by

⛏️ 7aRzAbv8pzf1A44ES9RdtZpBP4z1zat4zPXDTV

Merkle Root

36fd9d59625c89364102809b4f5a4b14a29261fd5e93557ed4882493607a0ddb

Transactions (4)

Coinbase0aa1b9adfc7f45…22576cd0255851

1 in → 28 out10.0400 XPM1015 B

Abv8pzf1…t4zPXDTV AQyr8Lw3…hs4nt3Pn AT8Hz6zE…Vb6sVbmY AQmTPDxR…qwmJq2NW AP9eJ2CZ…eYfb95GN

dc78b2b564ab0b…295391a627cef8

6 in → 1 out789.0300 XPM932 B

AT8Hz6zE…Vb6sVbmY

7ec0ac233835e5…08f4fd239ac33b

4 in → 2 out42.5787 XPM670 B

AY6hPgen…qzgJVG1V AZNRU7vM…oehcPMLz

c513c278392634…8cf92499394a01

1 in → 2 out0.2910 XPM226 B

AKRrNNCA…RYdG7pGR AbzFKqAp…vgQ1dLbB

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.

3.647 × 10⁹⁷(98-digit number)

36478533073536614589…89697123308338453999

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

3.647 × 10⁹⁷(98-digit number)

36478533073536614589…89697123308338453999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.647 × 10⁹⁷(98-digit number)

36478533073536614589…89697123308338454001

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

7.295 × 10⁹⁷(98-digit number)

72957066147073229179…79394246616676907999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.295 × 10⁹⁷(98-digit number)

72957066147073229179…79394246616676908001

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

1.459 × 10⁹⁸(99-digit number)

14591413229414645835…58788493233353815999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.459 × 10⁹⁸(99-digit number)

14591413229414645835…58788493233353816001

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

2.918 × 10⁹⁸(99-digit number)

29182826458829291671…17576986466707631999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.918 × 10⁹⁸(99-digit number)

29182826458829291671…17576986466707632001

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

5.836 × 10⁹⁸(99-digit number)

58365652917658583343…35153972933415263999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #276,458

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