Block #68,017

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/20/2013, 1:59:49 AM · Difficulty 8.9889 · 6,726,170 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6d4079fb204a54863121bfa749109a59c3c7fabda74ddc7ba356c43ab123c96b

View on Chainz ↗

Height

#68,017

Difficulty

8.988860

Transactions

Size

2.14 KB

Version

Bits

08fd25f3

Nonce

242

Timestamp

7/20/2013, 1:59:49 AM

Confirmations

6,726,170

Merkle Root

8f1c77126be9d4c2ec1353da16a16a67c1f314454272bf543fec8fc2a95c09f1

Transactions (2)

Coinbase95b2f8494ba218…ff72e8861e3f0e

1 in → 1 out12.3900 XPM110 B

AXSFye4r…ADf1YWCU

11b07f753b40b6…40aa2ec8a4744b

17 in → 1 out229.9600 XPM1.94 KB

AQw5658i…z9goLkPj

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.

9.592 × 10⁹⁵(96-digit number)

95924610078323311491…65377173318289603049

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

9.592 × 10⁹⁵(96-digit number)

95924610078323311491…65377173318289603049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.592 × 10⁹⁵(96-digit number)

95924610078323311491…65377173318289603051

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

1.918 × 10⁹⁶(97-digit number)

19184922015664662298…30754346636579206099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.918 × 10⁹⁶(97-digit number)

19184922015664662298…30754346636579206101

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

3.836 × 10⁹⁶(97-digit number)

38369844031329324596…61508693273158412199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.836 × 10⁹⁶(97-digit number)

38369844031329324596…61508693273158412201

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

7.673 × 10⁹⁶(97-digit number)

76739688062658649192…23017386546316824399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.673 × 10⁹⁶(97-digit number)

76739688062658649192…23017386546316824401

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

1.534 × 10⁹⁷(98-digit number)

15347937612531729838…46034773092633648799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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