Block #1,972,088

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/6/2017, 7:54:08 PM · Difficulty 10.7545 · 4,842,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

bf26a51100a4a4107de7c5c7ebfd34b53ca8b6ec034d8734734e49bb5fd5e833

View on Chainz ↗

Height

#1,972,088

Difficulty

10.754501

Transactions

Size

3.50 KB

Version

Bits

0ac126f3

Nonce

565,656,779

Timestamp

2/6/2017, 7:54:08 PM

Confirmations

4,842,750

Mined by

⛏️ P2SHAaCyGN8tPcC351kwVssPjAa7pP2SzpBuEi

Merkle Root

99bac17ca8dc19eb1f1262bd31666aac6579b5ec93438de820b804d509551d86

Transactions (2)

Coinbasef0e7f2eaa93f68…1de906029f5e16

1 in → 1 out8.6700 XPM110 B

AaCyGN8t…2SzpBuEi

165ab1c60951a0…a0f5bb46735c10

1 in → 95 out111.8845 XPM3.31 KB

AG39mvU8…Hvhkxi4w ANXhMoHH…dwFK1fhs AKGieKeJ…xW5m2auG ARmZWAA8…Y5VvZNk6 AZsfDcWa…xRkZWqrQ

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.

1.744 × 10⁹⁴(95-digit number)

17446706538798672318…28420534512001221919

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

1.744 × 10⁹⁴(95-digit number)

17446706538798672318…28420534512001221919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.744 × 10⁹⁴(95-digit number)

17446706538798672318…28420534512001221921

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

3.489 × 10⁹⁴(95-digit number)

34893413077597344637…56841069024002443839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.489 × 10⁹⁴(95-digit number)

34893413077597344637…56841069024002443841

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

6.978 × 10⁹⁴(95-digit number)

69786826155194689275…13682138048004887679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.978 × 10⁹⁴(95-digit number)

69786826155194689275…13682138048004887681

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

1.395 × 10⁹⁵(96-digit number)

13957365231038937855…27364276096009775359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.395 × 10⁹⁵(96-digit number)

13957365231038937855…27364276096009775361

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

2.791 × 10⁹⁵(96-digit number)

27914730462077875710…54728552192019550719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.791 × 10⁹⁵(96-digit number)

27914730462077875710…54728552192019550721

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

5.582 × 10⁹⁵(96-digit number)

55829460924155751420…09457104384039101439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #1,972,088

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