Block #230,608

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/27/2013, 10:11:27 PM · Difficulty 9.9397 · 6,580,286 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ce6eade336e0eb24273bcc0865f3e5805e0b07b30f67d50a7700cc40d643e0e6

View on Chainz ↗

Height

#230,608

Difficulty

9.939725

Transactions

Size

1.31 KB

Version

Bits

09f091d8

Nonce

49,677

Timestamp

10/27/2013, 10:11:27 PM

Confirmations

6,580,286

Mined by

⛏️ RmAGPBDvpY1KAcAHcLEXgAxzjSDhHsUDJ9oq

Merkle Root

547e747a36ff0f3f56655225ad6b0b9396bf386a574c7546c78b9abb07321ad3

Transactions (1)

Coinbase547e747a36ff0f…8b9abb07321ad3

1 in → 35 out10.0900 XPM1.22 KB

AGPBDvpY…HsUDJ9oq APw6W8tk…RgVVbThY AMbCuLHZ…WSoStwkc AU3PaCwF…92DCmeEV AWCfnjpk…hb1ovL8F

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.

5.013 × 10⁹⁶(97-digit number)

50137504480420015150…33080344971156025599

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

5.013 × 10⁹⁶(97-digit number)

50137504480420015150…33080344971156025599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.013 × 10⁹⁶(97-digit number)

50137504480420015150…33080344971156025601

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

1.002 × 10⁹⁷(98-digit number)

10027500896084003030…66160689942312051199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.002 × 10⁹⁷(98-digit number)

10027500896084003030…66160689942312051201

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

2.005 × 10⁹⁷(98-digit number)

20055001792168006060…32321379884624102399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.005 × 10⁹⁷(98-digit number)

20055001792168006060…32321379884624102401

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

4.011 × 10⁹⁷(98-digit number)

40110003584336012120…64642759769248204799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.011 × 10⁹⁷(98-digit number)

40110003584336012120…64642759769248204801

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

8.022 × 10⁹⁷(98-digit number)

80220007168672024240…29285519538496409599

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 #230,608

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