Block #547,401

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/16/2014, 11:27:20 AM · Difficulty 10.9570 · 6,267,489 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b15c1ef2e93809087c5905f6d3fde85fdca5f1b809cee1388f180156d6f53cf8

View on Chainz ↗

Height

#547,401

Difficulty

10.957013

Transactions

Size

664 B

Version

Bits

0af4fed4

Nonce

167,193

Timestamp

5/16/2014, 11:27:20 AM

Confirmations

6,267,489

Mined by

⛏️ IZaSuAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

3788dfbeff1669e2122bc31e524e3ec449e141c0675741f4b9b08a7d8c73a3fb

Transactions (1)

Coinbase3788dfbeff1669…b08a7d8c73a3fb

1 in → 15 out8.3200 XPM573 B

AQvZBsUo…hppgRZTJ AdxPNkWD…ZMa9u34q AUbecsVa…i8zo8qRf AJtNW28X…Syb4Ph5j AQyr8Lw3…hs4nt3Pn

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.

2.942 × 10⁹⁷(98-digit number)

29429009267352993599…85115956784830929039

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

2.942 × 10⁹⁷(98-digit number)

29429009267352993599…85115956784830929039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.942 × 10⁹⁷(98-digit number)

29429009267352993599…85115956784830929041

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

5.885 × 10⁹⁷(98-digit number)

58858018534705987199…70231913569661858079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.885 × 10⁹⁷(98-digit number)

58858018534705987199…70231913569661858081

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

1.177 × 10⁹⁸(99-digit number)

11771603706941197439…40463827139323716159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.177 × 10⁹⁸(99-digit number)

11771603706941197439…40463827139323716161

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

2.354 × 10⁹⁸(99-digit number)

23543207413882394879…80927654278647432319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.354 × 10⁹⁸(99-digit number)

23543207413882394879…80927654278647432321

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

4.708 × 10⁹⁸(99-digit number)

47086414827764789759…61855308557294864639

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.708 × 10⁹⁸(99-digit number)

47086414827764789759…61855308557294864641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

9.417 × 10⁹⁸(99-digit number)

94172829655529579519…23710617114589729279

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #547,401

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