Block #270,139

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 5:50:32 PM · Difficulty 9.9518 · 6,540,045 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4c4d7f7345ac2c694e57a562796bef481df08f0f06354ac51c88158333653b93

View on Chainz ↗

Height

#270,139

Difficulty

9.951775

Transactions

Size

2.11 KB

Version

Bits

09f3a78b

Nonce

209,537

Timestamp

11/23/2013, 5:50:32 PM

Confirmations

6,540,045

Mined by

⛏️ ;aRATKK7iFzxU98qfet38JZnUDJ7swZm46KN1

Merkle Root

9b0de3f5f8d17e07226cfd0e678eaa2d72d01aba806fe76974fcd727f371fab7

Transactions (1)

Coinbase9b0de3f5f8d17e…fcd727f371fab7

1 in → 59 out10.0500 XPM2.02 KB

ATKK7iFz…wZm46KN1 AdC8NfKe…9csBTCUH AdnG9gQ7…N9B7mA2p AHTTUHKB…g8V7VRLq AVzhvfTX…ZzNJYq61

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.

4.807 × 10⁹⁵(96-digit number)

48077968315181565405…11885917860556144639

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

4.807 × 10⁹⁵(96-digit number)

48077968315181565405…11885917860556144639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.807 × 10⁹⁵(96-digit number)

48077968315181565405…11885917860556144641

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

9.615 × 10⁹⁵(96-digit number)

96155936630363130811…23771835721112289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.615 × 10⁹⁵(96-digit number)

96155936630363130811…23771835721112289281

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

1.923 × 10⁹⁶(97-digit number)

19231187326072626162…47543671442224578559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.923 × 10⁹⁶(97-digit number)

19231187326072626162…47543671442224578561

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

3.846 × 10⁹⁶(97-digit number)

38462374652145252324…95087342884449157119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.846 × 10⁹⁶(97-digit number)

38462374652145252324…95087342884449157121

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

7.692 × 10⁹⁶(97-digit number)

76924749304290504649…90174685768898314239

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 #270,139

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