Block #348,109

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/7/2014, 2:46:17 PM · Difficulty 10.2501 · 6,446,242 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

006202d18a8e6c0590c20da341c28a4c27ab13e540c011de57ea3be8870827d2

View on Chainz ↗

Height

#348,109

Difficulty

10.250059

Transactions

Size

1.05 KB

Version

Bits

0a4003e3

Nonce

546

Timestamp

1/7/2014, 2:46:17 PM

Confirmations

6,446,242

Merkle Root

7f7c205c11a6efb2505e452608c6dc3ba15700e33e917057fd2631cd4f093a51

Transactions (1)

Coinbase7f7c205c11a6ef…2631cd4f093a51

1 in → 27 out9.5000 XPM981 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AUnkFe8H…fvenjA4X AZV4TwxQ…8JnQqSoH ARkHWBbk…NFGu7Vm7

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.

5.923 × 10⁹⁶(97-digit number)

59237375499715928696…14375131809652719999

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

5.923 × 10⁹⁶(97-digit number)

59237375499715928696…14375131809652719999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.923 × 10⁹⁶(97-digit number)

59237375499715928696…14375131809652720001

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

1.184 × 10⁹⁷(98-digit number)

11847475099943185739…28750263619305439999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.184 × 10⁹⁷(98-digit number)

11847475099943185739…28750263619305440001

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

2.369 × 10⁹⁷(98-digit number)

23694950199886371478…57500527238610879999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.369 × 10⁹⁷(98-digit number)

23694950199886371478…57500527238610880001

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

4.738 × 10⁹⁷(98-digit number)

47389900399772742957…15001054477221759999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.738 × 10⁹⁷(98-digit number)

47389900399772742957…15001054477221760001

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

9.477 × 10⁹⁷(98-digit number)

94779800799545485915…30002108954443519999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.477 × 10⁹⁷(98-digit number)

94779800799545485915…30002108954443520001

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