Block #354,690

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/11/2014, 4:50:47 PM · Difficulty 10.3483 · 6,460,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec70b82eaf69c3c5e155d330decfe90c1bb37367c8cb4f41b95dc5725648f2d5

View on Chainz ↗

Height

#354,690

Difficulty

10.348345

Transactions

Size

1.08 KB

Version

Bits

0a592d20

Nonce

6,736

Timestamp

1/11/2014, 4:50:47 PM

Confirmations

6,460,233

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

589f85426dadcaae81966bc64cfa6c1bfce778072fa26fa34273706b0247b58a

Transactions (5)

Coinbase576bfde61212ea…39906000ac3ac3

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

161f4b6dae5e65…5330b12a8989be

1 in → 2 out3.1646 XPM227 B

AdiAcsDb…ny9MCogr ASugE9k9…3APMrFm7

756ff08dbf1bb6…b4d79692712938

1 in → 2 out2.0526 XPM225 B

AN8kTRzC…TAxV79HA Ab8EFbuZ…2E8cPmVZ

46c39d1be23dde…8f7bc5af4134c0

1 in → 2 out2.0878 XPM226 B

AVR9s4fa…AW7C55ZT AaSZMhZy…k4vewrJy

0452900739cea6…272d6e018abb83

1 in → 2 out2.7200 XPM227 B

ATLBWLcU…yXfioiU6 AbBVnRm7…DrqYqbp8

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.

7.434 × 10⁹²(93-digit number)

74346123122815051990…64292751656177840549

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

7.434 × 10⁹²(93-digit number)

74346123122815051990…64292751656177840549

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.434 × 10⁹²(93-digit number)

74346123122815051990…64292751656177840551

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

1.486 × 10⁹³(94-digit number)

14869224624563010398…28585503312355681099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.486 × 10⁹³(94-digit number)

14869224624563010398…28585503312355681101

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

2.973 × 10⁹³(94-digit number)

29738449249126020796…57171006624711362199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.973 × 10⁹³(94-digit number)

29738449249126020796…57171006624711362201

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

5.947 × 10⁹³(94-digit number)

59476898498252041592…14342013249422724399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.947 × 10⁹³(94-digit number)

59476898498252041592…14342013249422724401

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

1.189 × 10⁹⁴(95-digit number)

11895379699650408318…28684026498845448799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.189 × 10⁹⁴(95-digit number)

11895379699650408318…28684026498845448801

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 #354,690

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