Block #1,670,640

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/13/2016, 2:49:29 AM · Difficulty 10.6934 · 5,154,214 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93d9da3a25061bd351de37839ddac518cf1fa10c7ce189fc4e057597984ab6f1

View on Chainz ↗

Height

#1,670,640

Difficulty

10.693408

Transactions

Size

663 B

Version

Bits

0ab18337

Nonce

674,589,648

Timestamp

7/13/2016, 2:49:29 AM

Confirmations

5,154,214

Mined by

⛏️ P2SHAGdqJ4Rr5dRBnSZH2GJjLPor4yHixwtYpw

Merkle Root

e576e0583137e64f3291c1d9ca25a1673d42aa6a89ac0e0267b40655bce6f936

Transactions (2)

Coinbase3619aba76a7165…ee9ad9a9131033

1 in → 1 out8.7400 XPM109 B

AGdqJ4Rr…HixwtYpw

16fdff606c3339…e9dc4d5ef051c0

1 in → 10 out8.7100 XPM464 B

AeBwvm57…kL6E7ayF ALqEZWdP…6VPV6ooe AWVdqMHf…3TnrQBYd AVvA9Gzu…7fxjvGRS AWE7WWq2…XHoZXbgN

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.

1.055 × 10⁹⁴(95-digit number)

10557953950402975328…26272320095855702079

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

1.055 × 10⁹⁴(95-digit number)

10557953950402975328…26272320095855702079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.055 × 10⁹⁴(95-digit number)

10557953950402975328…26272320095855702081

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

2.111 × 10⁹⁴(95-digit number)

21115907900805950657…52544640191711404159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.111 × 10⁹⁴(95-digit number)

21115907900805950657…52544640191711404161

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

4.223 × 10⁹⁴(95-digit number)

42231815801611901315…05089280383422808319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.223 × 10⁹⁴(95-digit number)

42231815801611901315…05089280383422808321

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

8.446 × 10⁹⁴(95-digit number)

84463631603223802630…10178560766845616639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.446 × 10⁹⁴(95-digit number)

84463631603223802630…10178560766845616641

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

1.689 × 10⁹⁵(96-digit number)

16892726320644760526…20357121533691233279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.689 × 10⁹⁵(96-digit number)

16892726320644760526…20357121533691233281

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 #1,670,640

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