Block #346,296

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/6/2014, 11:19:20 AM · Difficulty 10.2247 · 6,453,039 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

46f040849432dfc3c71896d13633b6fbe026d25accfd7afd7fab967588a242d9

View on Chainz ↗

Height

#346,296

Difficulty

10.224698

Transactions

Size

13.79 KB

Version

Bits

0a3985d6

Nonce

65,033

Timestamp

1/6/2014, 11:19:20 AM

Confirmations

6,453,039

Mined by

⛏️ P2SHAUzQArjcWkDC6kf6mmEqGmDLmKs1SyLXPk

Merkle Root

a286b90c88c434e37f8e2d7a38331c0dbbb0d3ccfbbfd52c827081a5877e9393

Transactions (3)

Coinbase9dc9cc37a22b11…482b8432c81c94

1 in → 1 out9.7000 XPM109 B

AUzQArjc…s1SyLXPk

978ee2ba5e8b63…4085b91ebb8d04

91 in → 2 out35.9730 XPM13.23 KB

AeBTGtEm…3SVLn2QU AFnapP1P…p1J8qMjV

1a707dc1efdfd6…047f582f5c3785

2 in → 2 out1.0185 XPM374 B

ATN6NnUD…Y7C9eC9A AYKNXPrs…MPPeqWKr

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.

3.741 × 10¹⁰⁵(106-digit number)

37415874140063958634…07664707029508546559

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

3.741 × 10¹⁰⁵(106-digit number)

37415874140063958634…07664707029508546559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.741 × 10¹⁰⁵(106-digit number)

37415874140063958634…07664707029508546561

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

7.483 × 10¹⁰⁵(106-digit number)

74831748280127917269…15329414059017093119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.483 × 10¹⁰⁵(106-digit number)

74831748280127917269…15329414059017093121

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

1.496 × 10¹⁰⁶(107-digit number)

14966349656025583453…30658828118034186239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.496 × 10¹⁰⁶(107-digit number)

14966349656025583453…30658828118034186241

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

2.993 × 10¹⁰⁶(107-digit number)

29932699312051166907…61317656236068372479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.993 × 10¹⁰⁶(107-digit number)

29932699312051166907…61317656236068372481

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

5.986 × 10¹⁰⁶(107-digit number)

59865398624102333815…22635312472136744959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.986 × 10¹⁰⁶(107-digit number)

59865398624102333815…22635312472136744961

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