Block #544,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2014, 9:16:49 PM · Difficulty 10.9505 · 6,261,585 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f52ba8fe0660c083d9a525582771dbdf86e69cf7b9946aa6c0138b18cd89d65

View on Chainz ↗

Height

#544,414

Difficulty

10.950484

Transactions

Size

845 B

Version

Bits

0af352ea

Nonce

114,961,822

Timestamp

5/14/2014, 9:16:49 PM

Confirmations

6,261,585

Mined by

⛏️ P2SHAWG3FawZDQZxJJT5yedTA3mvmZR4LVDR1Q

Merkle Root

9684259b370de119167043693ae3375f07e2216fa31771681ae9fc2991191779

Transactions (4)

Coinbase812d2df6aeb3fc…a09cdc7cdd6f82

1 in → 1 out8.3600 XPM109 B

AWG3FawZ…R4LVDR1Q

0f76319463523e…aa5d58a19e44b2

1 in → 2 out8.3900 XPM193 B

AeKNrjNj…1NEq95Ta AY1FuBSV…jEZrVd1U

d9ca85d369170b…e795fb209bfc90

1 in → 2 out6.2556 XPM226 B

ASc3rMkc…BgXLXK3f AQ2N9XsY…xMEug4ir

4c1a9b153235b8…12e325183a42f0

1 in → 2 out5.7403 XPM226 B

AZxkSxov…9uoWycVz AYZgZwmy…28ZpfhR2

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.

1.508 × 10⁹⁶(97-digit number)

15088660960980611357…54639229488137763839

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

1.508 × 10⁹⁶(97-digit number)

15088660960980611357…54639229488137763839

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.508 × 10⁹⁶(97-digit number)

15088660960980611357…54639229488137763841

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

3.017 × 10⁹⁶(97-digit number)

30177321921961222715…09278458976275527679

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.017 × 10⁹⁶(97-digit number)

30177321921961222715…09278458976275527681

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

6.035 × 10⁹⁶(97-digit number)

60354643843922445431…18556917952551055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.035 × 10⁹⁶(97-digit number)

60354643843922445431…18556917952551055361

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

1.207 × 10⁹⁷(98-digit number)

12070928768784489086…37113835905102110719

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.207 × 10⁹⁷(98-digit number)

12070928768784489086…37113835905102110721

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

2.414 × 10⁹⁷(98-digit number)

24141857537568978172…74227671810204221439

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.414 × 10⁹⁷(98-digit number)

24141857537568978172…74227671810204221441

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