Block #481,869

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/9/2014, 3:59:30 AM · Difficulty 10.5369 · 6,313,049 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5d645481be74c4208c2be3644f5e5e33cdb20b3d7df3c9393879aa63e4cd71af

View on Chainz ↗

Height

#481,869

Difficulty

10.536870

Transactions

Size

1.51 KB

Version

Bits

0a897051

Nonce

22,138

Timestamp

4/9/2014, 3:59:30 AM

Confirmations

6,313,049

Mined by

⛏️ MZaSD_AQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

32191dc340816891f94c03a09538612838370d71c27cfcc30077af26c7b92799

Transactions (4)

Coinbase5633a6ca7ea704…16233fc3dc993e

1 in → 21 out8.9900 XPM777 B

AQvZBsUo…hppgRZTJ AHwvxqCN…7z7foF67 AQ8QAT3J…rCFKuVbR ATKK7iFz…wZm46KN1 AWMrD5hP…ZwsoxvZ3

48e10a0d3c2159…060b5275e7b15b

1 in → 2 out4.9499 XPM226 B

AY6grhds…KdvSq2Xs AVoTn4bj…zZ465BGu

585bafc7f29d8c…eff5415e5f6d9f

1 in → 2 out1.2505 XPM225 B

AHhoGKVx…RoFhpcde AcgutXdx…p3jCPHGa

ad1f6b3d94bcd6…1f15a76cca2be0

1 in → 2 out4.9286 XPM226 B

ARUNx2MF…2QvQqZ4v AeEpqMsk…khoKB2a5

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.

2.257 × 10⁹⁷(98-digit number)

22576908247203161048…78101471019135161439

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

2.257 × 10⁹⁷(98-digit number)

22576908247203161048…78101471019135161439

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.257 × 10⁹⁷(98-digit number)

22576908247203161048…78101471019135161441

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

4.515 × 10⁹⁷(98-digit number)

45153816494406322096…56202942038270322879

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.515 × 10⁹⁷(98-digit number)

45153816494406322096…56202942038270322881

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

9.030 × 10⁹⁷(98-digit number)

90307632988812644193…12405884076540645759

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.030 × 10⁹⁷(98-digit number)

90307632988812644193…12405884076540645761

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

1.806 × 10⁹⁸(99-digit number)

18061526597762528838…24811768153081291519

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.806 × 10⁹⁸(99-digit number)

18061526597762528838…24811768153081291521

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

3.612 × 10⁹⁸(99-digit number)

36123053195525057677…49623536306162583039

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.612 × 10⁹⁸(99-digit number)

36123053195525057677…49623536306162583041

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