Block #1,968,731

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/4/2017, 1:05:25 PM · Difficulty 10.7510 · 4,875,983 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

195781d083614626a433d3eb56a858c3a18ffcaf8d11783556edc6e489bc4eef

View on Chainz ↗

Height

#1,968,731

Difficulty

10.751012

Transactions

Size

1.14 KB

Version

Bits

0ac04252

Nonce

484,466,784

Timestamp

2/4/2017, 1:05:25 PM

Confirmations

4,875,983

Mined by

⛏️ P2SHAchcyDoNKHGcPDFCHKJhzhsWXP7LVeDGAu

Merkle Root

ef342d062317b1a6e15205f3e91f4b647e8f77d2eb5fe21edf50f59e7dc1c666

Transactions (2)

Coinbasee94b3870332a16…b91bd9b3698ca6

1 in → 1 out8.6500 XPM109 B

AchcyDoN…7LVeDGAu

b6b73606ca8b07…dec87f9bf7e531

6 in → 2 out146.9666 XPM965 B

AbSihS6q…PPdLXDv8 AY4uVaSB…EBcEXcuM

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.

1.964 × 10⁹⁶(97-digit number)

19649199569821040405…65323320745694105599

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

1.964 × 10⁹⁶(97-digit number)

19649199569821040405…65323320745694105599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.964 × 10⁹⁶(97-digit number)

19649199569821040405…65323320745694105601

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

3.929 × 10⁹⁶(97-digit number)

39298399139642080810…30646641491388211199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.929 × 10⁹⁶(97-digit number)

39298399139642080810…30646641491388211201

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

7.859 × 10⁹⁶(97-digit number)

78596798279284161621…61293282982776422399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.859 × 10⁹⁶(97-digit number)

78596798279284161621…61293282982776422401

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

1.571 × 10⁹⁷(98-digit number)

15719359655856832324…22586565965552844799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.571 × 10⁹⁷(98-digit number)

15719359655856832324…22586565965552844801

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

3.143 × 10⁹⁷(98-digit number)

31438719311713664648…45173131931105689599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.143 × 10⁹⁷(98-digit number)

31438719311713664648…45173131931105689601

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 #1,968,731

Cookie Preferences