Block #99,249

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/5/2013, 2:39:31 PM · Difficulty 9.3796 · 6,692,169 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9a4e89816c5edf21450e96570be56efbe9e47707422efa267bc0bc7ab96c3298

View on Chainz ↗

Height

#99,249

Difficulty

9.379648

Transactions

Size

200 B

Version

Bits

09613098

Nonce

205,495

Timestamp

8/5/2013, 2:39:31 PM

Confirmations

6,692,169

Merkle Root

0e4f838115aca4581668154c264437f08eea776f4cfc1bbf9787d9b1938be7ea

Transactions (1)

Coinbase0e4f838115aca4…87d9b1938be7ea

1 in → 1 out11.3500 XPM109 B

AWuDuxGX…tLDpHWp7

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.

8.112 × 10⁹⁷(98-digit number)

81125827448557838968…51229824904192749679

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

8.112 × 10⁹⁷(98-digit number)

81125827448557838968…51229824904192749679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.112 × 10⁹⁷(98-digit number)

81125827448557838968…51229824904192749681

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

1.622 × 10⁹⁸(99-digit number)

16225165489711567793…02459649808385499359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.622 × 10⁹⁸(99-digit number)

16225165489711567793…02459649808385499361

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

3.245 × 10⁹⁸(99-digit number)

32450330979423135587…04919299616770998719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.245 × 10⁹⁸(99-digit number)

32450330979423135587…04919299616770998721

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

6.490 × 10⁹⁸(99-digit number)

64900661958846271174…09838599233541997439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.490 × 10⁹⁸(99-digit number)

64900661958846271174…09838599233541997441

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

1.298 × 10⁹⁹(100-digit number)

12980132391769254234…19677198467083994879

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