Block #270,321

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/23/2013, 8:43:45 PM · Difficulty 9.9519 · 6,546,460 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6dae0656bcba5092036509a3668e7f61886030290d23c0f367f10de99d3e3ec3

View on Chainz ↗

Height

#270,321

Difficulty

9.951853

Transactions

Size

2.48 KB

Version

Bits

09f3ac9e

Nonce

7,392

Timestamp

11/23/2013, 8:43:45 PM

Confirmations

6,546,460

Mined by

⛏️ aRARXSrG7zDJaFCruTxsaP6YvsvPCRW69WR4

Merkle Root

700d807e68302633c6f71e282066fe84b70fa72e08fd23d471dc30036438204c

Transactions (4)

Coinbaseb83c5c52d5dc88…653c2d8a054b98

1 in → 46 out10.0600 XPM1.59 KB

ARXSrG7z…CRW69WR4 ANmkKL2U…jPxj1Qs3 AdL4ZZDR…2eQtg1T9 AHqZtsfn…WrCGjM3J AVzhvfTX…ZzNJYq61

ecc6caeba588c0…6d052bb0d20a50

2 in → 2 out20.1200 XPM376 B

AdWp2YRv…FDtt217a Af63frK4…FD6dcqxc

5c8d5ddb0f8d2a…75ee46fbcf5f6d

1 in → 2 out9.7300 XPM226 B

AS5296h3…5cpuVeAe AWKhcKD1…AK1RJ4a3

bb9ab1e9940200…968f9db15d1a69

1 in → 2 out5.9695 XPM225 B

AXJ8XAj9…sCUvU14n AY6yXsX4…DCFFkJYV

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.

7.331 × 10⁹⁵(96-digit number)

73313851398455952624…70713237994057316959

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

7.331 × 10⁹⁵(96-digit number)

73313851398455952624…70713237994057316959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.331 × 10⁹⁵(96-digit number)

73313851398455952624…70713237994057316961

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

1.466 × 10⁹⁶(97-digit number)

14662770279691190524…41426475988114633919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.466 × 10⁹⁶(97-digit number)

14662770279691190524…41426475988114633921

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

2.932 × 10⁹⁶(97-digit number)

29325540559382381049…82852951976229267839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.932 × 10⁹⁶(97-digit number)

29325540559382381049…82852951976229267841

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

5.865 × 10⁹⁶(97-digit number)

58651081118764762099…65705903952458535679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.865 × 10⁹⁶(97-digit number)

58651081118764762099…65705903952458535681

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

1.173 × 10⁹⁷(98-digit number)

11730216223752952419…31411807904917071359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.173 × 10⁹⁷(98-digit number)

11730216223752952419…31411807904917071361

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #270,321

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