Block #270,296

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 8:19:53 PM · Difficulty 9.9518 · 6,556,804 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9202df5f92039003ec0f9e7300bdaed39501bd9f8eadce2efff7904f3fab10fc

View on Chainz ↗

Height

#270,296

Difficulty

9.951848

Transactions

Size

1.91 KB

Version

Bits

09f3ac4a

Nonce

187,781

Timestamp

11/23/2013, 8:19:53 PM

Confirmations

6,556,804

Mined by

⛏️ aRALdHh27brbEqnGMrZaaR18HaaAXNbqrvPf

Merkle Root

1b29411446a1427c45af97c9a3051d4d22b5e75f4f520dceb4742251a37dc736

Transactions (1)

Coinbase1b29411446a142…742251a37dc736

1 in → 53 out10.0600 XPM1.82 KB

ALdHh27b…XNbqrvPf AFqKfjez…qX9Ace3g AdnG9gQ7…N9B7mA2p ANHbaxZp…XjnHCJJs AWgqqfT4…UWpeKFh7

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.

2.675 × 10⁹²(93-digit number)

26756715151784505657…88838142732492665439

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

2.675 × 10⁹²(93-digit number)

26756715151784505657…88838142732492665439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.675 × 10⁹²(93-digit number)

26756715151784505657…88838142732492665441

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

5.351 × 10⁹²(93-digit number)

53513430303569011315…77676285464985330879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.351 × 10⁹²(93-digit number)

53513430303569011315…77676285464985330881

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

1.070 × 10⁹³(94-digit number)

10702686060713802263…55352570929970661759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.070 × 10⁹³(94-digit number)

10702686060713802263…55352570929970661761

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

2.140 × 10⁹³(94-digit number)

21405372121427604526…10705141859941323519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.140 × 10⁹³(94-digit number)

21405372121427604526…10705141859941323521

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

4.281 × 10⁹³(94-digit number)

42810744242855209052…21410283719882647039

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 #270,296

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