Block #547,722

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/16/2014, 3:34:09 PM · Difficulty 10.9576 · 6,279,282 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dbf546a4d1390860506392316fc85bb5131f674fa743c31b920a78d540444ce0

View on Chainz ↗

Height

#547,722

Difficulty

10.957595

Transactions

Size

658 B

Version

Bits

0af524f9

Nonce

141,824,797

Timestamp

5/16/2014, 3:34:09 PM

Confirmations

6,279,282

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ac5ed0159ce46d68ff884d8b186634701ad2242dc03fb0a0f7fae780865c52ea

Transactions (3)

Coinbase6e4a32b1cbea1a…a92495dd0b0319

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

ace59ca0d757ca…ce5d04fbc43968

1 in → 2 out5.1323 XPM225 B

AG8u7ddV…cU5QJSqk AZSSW5rT…wNW8bq9F

5400eacb188d8c…f1225bfeca72b0

1 in → 2 out4.5007 XPM225 B

AQj3K98w…Sszmm2Zt AGhYL2an…EZChTb64

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.

3.389 × 10⁹⁹(100-digit number)

33898421454355974067…56885099896938175359

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

3.389 × 10⁹⁹(100-digit number)

33898421454355974067…56885099896938175359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.389 × 10⁹⁹(100-digit number)

33898421454355974067…56885099896938175361

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

6.779 × 10⁹⁹(100-digit number)

67796842908711948135…13770199793876350719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.779 × 10⁹⁹(100-digit number)

67796842908711948135…13770199793876350721

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

1.355 × 10¹⁰⁰(101-digit number)

13559368581742389627…27540399587752701439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.355 × 10¹⁰⁰(101-digit number)

13559368581742389627…27540399587752701441

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

2.711 × 10¹⁰⁰(101-digit number)

27118737163484779254…55080799175505402879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.711 × 10¹⁰⁰(101-digit number)

27118737163484779254…55080799175505402881

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

5.423 × 10¹⁰⁰(101-digit number)

54237474326969558508…10161598351010805759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.423 × 10¹⁰⁰(101-digit number)

54237474326969558508…10161598351010805761

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 #547,722

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