Block #273,968

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/26/2013, 1:58:25 AM · Difficulty 9.9561 · 6,536,796 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9d2c36d48f18bc50ff7db75a94404ae8d6d0f3bad119a75be630df7841dcbcef

View on Chainz ↗

Height

#273,968

Difficulty

9.956114

Transactions

Size

1.33 KB

Version

Bits

09f4c3e9

Nonce

236,954

Timestamp

11/26/2013, 1:58:25 AM

Confirmations

6,536,796

Mined by

⛏️ 0.aRAPeshfYVKJ2qg4aRhC5FMjPmxg3PKcKMKH

Merkle Root

4f313853fe9cecc6f2b52c1366aa6a34f60a7a3b6995ac6ddf8b4baa6eb40030

Transactions (2)

Coinbase5e51b47d9f46d7…a5b4423da42464

1 in → 29 out10.0500 XPM1.02 KB

APeshfYV…3PKcKMKH AN8nUzff…YcDfRDQ2 Abv8pzf1…t4zPXDTV AVzhvfTX…ZzNJYq61 ANuKx9Ke…wm7nrBRq

37ac2d6a91fdaa…07fd825ccc642e

1 in → 2 out6.0118 XPM226 B

AJWKjKdR…CeJh3MxA AQUPKg3x…SGiZwr3h

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.

1.090 × 10⁹³(94-digit number)

10903176404272936305…43456448131005941759

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

1.090 × 10⁹³(94-digit number)

10903176404272936305…43456448131005941759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.090 × 10⁹³(94-digit number)

10903176404272936305…43456448131005941761

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

2.180 × 10⁹³(94-digit number)

21806352808545872610…86912896262011883519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.180 × 10⁹³(94-digit number)

21806352808545872610…86912896262011883521

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

4.361 × 10⁹³(94-digit number)

43612705617091745221…73825792524023767039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.361 × 10⁹³(94-digit number)

43612705617091745221…73825792524023767041

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

8.722 × 10⁹³(94-digit number)

87225411234183490443…47651585048047534079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.722 × 10⁹³(94-digit number)

87225411234183490443…47651585048047534081

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

1.744 × 10⁹⁴(95-digit number)

17445082246836698088…95303170096095068159

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 #273,968

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