Block #547,297

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2014, 9:45:58 AM · Difficulty 10.9569 · 6,269,799 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6707b7a5db9e357fd28bde61c08435830013a46b03eb624ae835e72a5589e697

View on Chainz ↗

Height

#547,297

Difficulty

10.956930

Transactions

Size

1.22 KB

Version

Bits

0af4f958

Nonce

350,059,015

Timestamp

5/16/2014, 9:45:58 AM

Confirmations

6,269,799

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1dfee61223efb709b2a3d4985dc4accb5b8dbfb69c8306321b1ea50e3fa39dc9

Transactions (3)

Coinbase1ad1ee018378e4…8d811e13f285a5

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

3851fda4ec736b…c89ef650741f46

5 in → 2 out1.3325 XPM817 B

ATD3HkET…Hv1EFBLX APXncyu3…1zTtrnZA

5ff68a33c00f5a…c09963017799c0

1 in → 2 out5.2743 XPM226 B

AVuR57uD…qdXNw3x1 AeKNrjNj…1NEq95Ta

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.

7.197 × 10⁹⁷(98-digit number)

71970866916730264414…03436540628866341279

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

7.197 × 10⁹⁷(98-digit number)

71970866916730264414…03436540628866341279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.197 × 10⁹⁷(98-digit number)

71970866916730264414…03436540628866341281

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

1.439 × 10⁹⁸(99-digit number)

14394173383346052882…06873081257732682559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.439 × 10⁹⁸(99-digit number)

14394173383346052882…06873081257732682561

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

2.878 × 10⁹⁸(99-digit number)

28788346766692105765…13746162515465365119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.878 × 10⁹⁸(99-digit number)

28788346766692105765…13746162515465365121

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

5.757 × 10⁹⁸(99-digit number)

57576693533384211531…27492325030930730239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.757 × 10⁹⁸(99-digit number)

57576693533384211531…27492325030930730241

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

1.151 × 10⁹⁹(100-digit number)

11515338706676842306…54984650061861460479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.151 × 10⁹⁹(100-digit number)

11515338706676842306…54984650061861460481

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

Block #547,297

Cookie Preferences