Block #199,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/8/2013, 1:45:10 PM · Difficulty 9.8880 · 6,592,961 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4d4564f4434357fd825d37e3bdeb4b856a6a58e0c1045adb6c3a9aba917c7ae5

View on Chainz ↗

Height

#199,729

Difficulty

9.888003

Transactions

Size

391 B

Version

Bits

09e35430

Nonce

9,450

Timestamp

10/8/2013, 1:45:10 PM

Confirmations

6,592,961

Merkle Root

89e5dcea0d72a1a726873480e48f39e0cec5cba027ee93c7e58f0569fb6786bd

Transactions (2)

Coinbase828f8590ffad66…8181038cb65a7b

1 in → 1 out10.2200 XPM109 B

ALaRq8vB…Q6eQZGh6

33b12d61626020…8d98ff0de923c2

1 in → 2 out10.2300 XPM192 B

AacQZCQ3…xLkfXnVn AFz9fXym…wh4UqpkL

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.

3.981 × 10⁹⁵(96-digit number)

39815677053201108039…87937058112387238399

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

3.981 × 10⁹⁵(96-digit number)

39815677053201108039…87937058112387238399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.981 × 10⁹⁵(96-digit number)

39815677053201108039…87937058112387238401

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

7.963 × 10⁹⁵(96-digit number)

79631354106402216078…75874116224774476799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.963 × 10⁹⁵(96-digit number)

79631354106402216078…75874116224774476801

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

1.592 × 10⁹⁶(97-digit number)

15926270821280443215…51748232449548953599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.592 × 10⁹⁶(97-digit number)

15926270821280443215…51748232449548953601

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

3.185 × 10⁹⁶(97-digit number)

31852541642560886431…03496464899097907199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.185 × 10⁹⁶(97-digit number)

31852541642560886431…03496464899097907201

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

6.370 × 10⁹⁶(97-digit number)

63705083285121772862…06992929798195814399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.370 × 10⁹⁶(97-digit number)

63705083285121772862…06992929798195814401

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