Block #350,911

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 9:05:38 AM · Difficulty 10.2890 · 6,458,502 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

855a51847e8f0a4629aca3c66d30dc4ac8982515529976945aee67a87ef97981

View on Chainz ↗

Height

#350,911

Difficulty

10.288976

Transactions

Size

2.03 KB

Version

Bits

0a49fa56

Nonce

15,514

Timestamp

1/9/2014, 9:05:38 AM

Confirmations

6,458,502

Mined by

⛏️ P2SHAJXDg61mRvCmvrqwW3TSyy6bhXnn9yYhbJ

Merkle Root

7f5992fb99c4b26dd066281f65999056ee94251f95340ea9e281875c391dfeb2

Transactions (5)

Coinbasef77a6c45fc0cff…a1470273935b6d

1 in → 1 out9.4800 XPM109 B

AJXDg61m…nn9yYhbJ

c5306787d5dc3f…e2a1d9fa02618b

5 in → 13 out39.1245 XPM1.03 KB

AM6mbsxm…26DZVcDa AYSwRnwG…4im2Y9vG Abu1uzTT…6jPtvXzW AWkTY9wW…HrBW1npq ANTGMD8n…pvc8NoeL

4c65b7ba31bad2…e5fbf32f89d507

2 in → 2 out5.2687 XPM374 B

AUWrX8nP…z8c4RV6L ARt78fXe…AMgCxJHH

2b6511e50b402a…3ce18a040a753d

1 in → 2 out2.4767 XPM225 B

AJAfJN15…9E7rrKfv AdmZmq4M…MSeVctfA

c9865987e5f99a…fbf0ce196062fe

1 in → 2 out2.3651 XPM225 B

AGjiJUqz…noYXu1sW AUFk7gDX…1or9bmAN

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.

1.648 × 10⁹⁶(97-digit number)

16481617170287730830…08113389704126521599

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

1.648 × 10⁹⁶(97-digit number)

16481617170287730830…08113389704126521599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.648 × 10⁹⁶(97-digit number)

16481617170287730830…08113389704126521601

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

3.296 × 10⁹⁶(97-digit number)

32963234340575461660…16226779408253043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.296 × 10⁹⁶(97-digit number)

32963234340575461660…16226779408253043201

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

6.592 × 10⁹⁶(97-digit number)

65926468681150923320…32453558816506086399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.592 × 10⁹⁶(97-digit number)

65926468681150923320…32453558816506086401

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

1.318 × 10⁹⁷(98-digit number)

13185293736230184664…64907117633012172799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.318 × 10⁹⁷(98-digit number)

13185293736230184664…64907117633012172801

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

2.637 × 10⁹⁷(98-digit number)

26370587472460369328…29814235266024345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.637 × 10⁹⁷(98-digit number)

26370587472460369328…29814235266024345601

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 #350,911

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