Block #374,480

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 1:32:16 AM · Difficulty 10.4227 · 6,440,469 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e43389158843330fff3bfba03c7b67dd0f6c06be678596dccc0a64b4559325a8

View on Chainz ↗

Height

#374,480

Difficulty

10.422747

Transactions

Size

624 B

Version

Bits

0a6c391e

Nonce

83,889,212

Timestamp

1/25/2014, 1:32:16 AM

Confirmations

6,440,469

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

19820ddf942a27bfd8b2dab4a0a4f179061305a70c968b3e7ead3854589beaea

Transactions (3)

Coinbaseea99a2143361b0…743a63b371f228

1 in → 1 out9.2100 XPM116 B

AbwWkWZt…kawDhufa

2fd10911b90caa…da286e5b62e210

1 in → 1 out0.9913 XPM191 B

AHixoKk8…HV5nDmvF

dc6d4d250b9ea4…63230671fb6bd4

1 in → 2 out2.0737 XPM226 B

ATowFNZU…DEUduzWg ANjEKycP…gJ7LxqnR

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.

1.333 × 10⁹⁶(97-digit number)

13335014628076998389…98528193891522150399

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

1.333 × 10⁹⁶(97-digit number)

13335014628076998389…98528193891522150399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10⁹⁶(97-digit number)

13335014628076998389…98528193891522150401

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

2.667 × 10⁹⁶(97-digit number)

26670029256153996779…97056387783044300799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.667 × 10⁹⁶(97-digit number)

26670029256153996779…97056387783044300801

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

5.334 × 10⁹⁶(97-digit number)

53340058512307993558…94112775566088601599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.334 × 10⁹⁶(97-digit number)

53340058512307993558…94112775566088601601

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

1.066 × 10⁹⁷(98-digit number)

10668011702461598711…88225551132177203199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.066 × 10⁹⁷(98-digit number)

10668011702461598711…88225551132177203201

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

2.133 × 10⁹⁷(98-digit number)

21336023404923197423…76451102264354406399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.133 × 10⁹⁷(98-digit number)

21336023404923197423…76451102264354406401

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 #374,480

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