Block #1,981,547

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/13/2017, 9:57:27 AM · Difficulty 10.7538 · 4,861,210 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f22a8dd3615241b13d14b4b16451acd00008986e5dda520b979cb4a3b651c218

View on Chainz ↗

Height

#1,981,547

Difficulty

10.753788

Transactions

Size

425 B

Version

Bits

0ac0f844

Nonce

1,193,890,366

Timestamp

2/13/2017, 9:57:27 AM

Confirmations

4,861,210

Mined by

⛏️ P2SHAdtKdvBo3VP1WL5UBXSz61c2BSKpky7emb

Merkle Root

5576c7e4dd8db09563b58ab3f7e0c733943623ab9b772c4bdff613549c1aeaee

Transactions (2)

Coinbasebc18e4755b36a2…d098c44e41d12f

1 in → 1 out8.6400 XPM109 B

AdtKdvBo…Kpky7emb

9835dd7c568339…09eabe337fbd3a

1 in → 2 out2300.6856 XPM225 B

AcByYFvF…uKstVbNS Aei8wyaa…2PmtoTHm

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.

1.161 × 10⁹⁶(97-digit number)

11612655001551654016…86047226531720481279

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

1.161 × 10⁹⁶(97-digit number)

11612655001551654016…86047226531720481279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.161 × 10⁹⁶(97-digit number)

11612655001551654016…86047226531720481281

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

2.322 × 10⁹⁶(97-digit number)

23225310003103308032…72094453063440962559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.322 × 10⁹⁶(97-digit number)

23225310003103308032…72094453063440962561

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

4.645 × 10⁹⁶(97-digit number)

46450620006206616065…44188906126881925119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.645 × 10⁹⁶(97-digit number)

46450620006206616065…44188906126881925121

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

9.290 × 10⁹⁶(97-digit number)

92901240012413232131…88377812253763850239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.290 × 10⁹⁶(97-digit number)

92901240012413232131…88377812253763850241

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

1.858 × 10⁹⁷(98-digit number)

18580248002482646426…76755624507527700479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.858 × 10⁹⁷(98-digit number)

18580248002482646426…76755624507527700481

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 #1,981,547

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