Block #518,484

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/30/2014, 3:22:28 PM · Difficulty 10.8533 · 6,278,145 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c7751110d104388841b07f8e1f8429c67657d02958a7dd1e8364b6b3fec06fd0

View on Chainz ↗

Height

#518,484

Difficulty

10.853343

Transactions

Size

1.23 KB

Version

Bits

0ada74ae

Nonce

114,670,099

Timestamp

4/30/2014, 3:22:28 PM

Confirmations

6,278,145

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

33ce1c4ad6a414b0cc39454e13bcc26494e34f8554ba5deba8e05f5a236ed0be

Transactions (5)

Coinbase22e3f029c60611…70b7ad7a06b2ed

1 in → 1 out8.5200 XPM116 B

AbwWkWZt…kawDhufa

cf4f9f6f7d8ebf…627f6ba55b1f2f

2 in → 2 out13.9523 XPM375 B

AGpCynbf…fPbwq2rh AWH2iBFw…bcztGS7x

6dd1d19f3fee7d…7e590266f1e649

1 in → 2 out6.9657 XPM226 B

AKUTbiz2…z8UsGRB1 AYU1Ynxb…6LNs2ZYM

99b6c82d4133ba…e5686f0fcf98b8

1 in → 2 out7.4611 XPM225 B

AGdWVjRk…LFVsqCnK ARDB1cDD…6eqpbAZx

8437907ff2edd3…3992f67605ad5a

1 in → 2 out6.8397 XPM226 B

AHft81SG…BTCFNTy8 Ad8ouZVy…Agtc4Bzk

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.

5.390 × 10⁹⁸(99-digit number)

53901310388638710521…76722778438393641719

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

5.390 × 10⁹⁸(99-digit number)

53901310388638710521…76722778438393641719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.390 × 10⁹⁸(99-digit number)

53901310388638710521…76722778438393641721

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

1.078 × 10⁹⁹(100-digit number)

10780262077727742104…53445556876787283439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.078 × 10⁹⁹(100-digit number)

10780262077727742104…53445556876787283441

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

2.156 × 10⁹⁹(100-digit number)

21560524155455484208…06891113753574566879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.156 × 10⁹⁹(100-digit number)

21560524155455484208…06891113753574566881

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

4.312 × 10⁹⁹(100-digit number)

43121048310910968417…13782227507149133759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.312 × 10⁹⁹(100-digit number)

43121048310910968417…13782227507149133761

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

8.624 × 10⁹⁹(100-digit number)

86242096621821936834…27564455014298267519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.624 × 10⁹⁹(100-digit number)

86242096621821936834…27564455014298267521

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