Block #270,156

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 6:05:44 PM · Difficulty 9.9518 · 6,570,157 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

de20e8583757767cd4d009e536a8dcfa4668a6deace4ea6e777b7ae601be97de

View on Chainz ↗

Height

#270,156

Difficulty

9.951781

Transactions

Size

871 B

Version

Bits

09f3a7e9

Nonce

420

Timestamp

11/23/2013, 6:05:44 PM

Confirmations

6,570,157

Mined by

⛏️ P2SHAdGRRh1eP4JFvQMqy7y2pLsryDQmctLb24

Merkle Root

bf15fadffbe9435331580ddd05b585207a140030d2229260b58160967e5191f6

Transactions (2)

Coinbasefc268c37a7fc3d…07643cf6c8411b

1 in → 2 out10.1000 XPM141 B

AdGRRh1e…QmctLb24 ALfEGCwh…VawujfMm

bd8f55a35d98ad…4cf068cebbf712

4 in → 1 out17.9800 XPM636 B

Ae7Gp2Gx…c3kUjvBU

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.

4.773 × 10¹⁰³(104-digit number)

47733535352868114171…24672286913740988799

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

4.773 × 10¹⁰³(104-digit number)

47733535352868114171…24672286913740988799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.773 × 10¹⁰³(104-digit number)

47733535352868114171…24672286913740988801

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

9.546 × 10¹⁰³(104-digit number)

95467070705736228343…49344573827481977599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.546 × 10¹⁰³(104-digit number)

95467070705736228343…49344573827481977601

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

1.909 × 10¹⁰⁴(105-digit number)

19093414141147245668…98689147654963955199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.909 × 10¹⁰⁴(105-digit number)

19093414141147245668…98689147654963955201

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

3.818 × 10¹⁰⁴(105-digit number)

38186828282294491337…97378295309927910399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.818 × 10¹⁰⁴(105-digit number)

38186828282294491337…97378295309927910401

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

7.637 × 10¹⁰⁴(105-digit number)

76373656564588982674…94756590619855820799

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 #270,156

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