Block #297,386

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/6/2013, 2:07:09 PM · Difficulty 9.9920 · 6,505,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c18b4e9f2ce3518b4d839896fa928d8ef183a4b552fb1005fd24c7795ecf1540

View on Chainz ↗

Height

#297,386

Difficulty

9.991955

Transactions

Size

1.08 KB

Version

Bits

09fdf0bf

Nonce

153,387

Timestamp

12/6/2013, 2:07:09 PM

Confirmations

6,505,409

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

294bb49191905f0bee3c87709d849df2f0c7b2de0ee89ff66e1205436463cad9

Transactions (5)

Coinbase2387a1150ccf49…b36685407c4d8d

1 in → 1 out10.0400 XPM110 B

AeKNrjNj…1NEq95Ta

ec97bca4cfc257…905ac30cd1603d

1 in → 2 out8.8790 XPM226 B

AQrCvMKV…Rt8xerNs APFe9JNh…z1HwLxgK

acb0cd6043a3da…5aa31b9a19e078

1 in → 2 out2.8118 XPM225 B

AdA1kNGN…gojTGyna AadRhjsa…mveq9caq

a1c32e50adafa2…c3fec45f8b6422

1 in → 2 out3.8348 XPM227 B

AN8RKugL…d6m3McZX AbN9LM17…KfBJFx8y

6bd001e223abdb…5f6b8de58bd5f9

1 in → 2 out3.7530 XPM227 B

AVBT19xX…HrBo7DLh AHWZS61u…jbAbxZLr

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.

1.908 × 10⁹⁷(98-digit number)

19084686415417908132…92253944624412917759

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

1.908 × 10⁹⁷(98-digit number)

19084686415417908132…92253944624412917759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.908 × 10⁹⁷(98-digit number)

19084686415417908132…92253944624412917761

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

3.816 × 10⁹⁷(98-digit number)

38169372830835816264…84507889248825835519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.816 × 10⁹⁷(98-digit number)

38169372830835816264…84507889248825835521

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

7.633 × 10⁹⁷(98-digit number)

76338745661671632529…69015778497651671039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.633 × 10⁹⁷(98-digit number)

76338745661671632529…69015778497651671041

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

1.526 × 10⁹⁸(99-digit number)

15267749132334326505…38031556995303342079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.526 × 10⁹⁸(99-digit number)

15267749132334326505…38031556995303342081

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

3.053 × 10⁹⁸(99-digit number)

30535498264668653011…76063113990606684159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.053 × 10⁹⁸(99-digit number)

30535498264668653011…76063113990606684161

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