Block #534,548

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/10/2014, 9:35:41 AM · Difficulty 10.9022 · 6,273,757 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

012b3327d26b272b8e63e33935b6552ac39e5e38df618a28e55d33c95813b10a

View on Chainz ↗

Height

#534,548

Difficulty

10.902168

Transactions

Size

884 B

Version

Bits

0ae6f475

Nonce

16,407,725

Timestamp

5/10/2014, 9:35:41 AM

Confirmations

6,273,757

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

81a51e35ddb61e77a8c7ac40cdf790d14f1b9833493b678cf97b3436b5657e0a

Transactions (4)

Coinbase3ee6fa577c5c19…013b0fc3e83c5b

1 in → 1 out8.4300 XPM116 B

ANSXnLY2…Sd25TjkD

38ac6d1199420e…494a07b21a5395

1 in → 3 out8.4000 XPM226 B

AeKNrjNj…1NEq95Ta AL48EMca…MMV6JRSc AcBvLaSu…X3gaHvJ1

76fb6821737b1c…0cb9db3c514ef1

1 in → 2 out7.2572 XPM225 B

ALdrEQ1j…UcSXLXxA AKweJ6z4…fiQLQ8zk

fa81636334b351…d6eff86ba61688

1 in → 2 out6.8467 XPM225 B

AXwNZCZW…5A19VLiM AG8u7ddV…cU5QJSqk

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.

7.595 × 10⁹⁸(99-digit number)

75952624218183957520…87059683550729600879

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

7.595 × 10⁹⁸(99-digit number)

75952624218183957520…87059683550729600879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.595 × 10⁹⁸(99-digit number)

75952624218183957520…87059683550729600881

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

1.519 × 10⁹⁹(100-digit number)

15190524843636791504…74119367101459201759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.519 × 10⁹⁹(100-digit number)

15190524843636791504…74119367101459201761

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

3.038 × 10⁹⁹(100-digit number)

30381049687273583008…48238734202918403519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.038 × 10⁹⁹(100-digit number)

30381049687273583008…48238734202918403521

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

6.076 × 10⁹⁹(100-digit number)

60762099374547166016…96477468405836807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.076 × 10⁹⁹(100-digit number)

60762099374547166016…96477468405836807041

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

1.215 × 10¹⁰⁰(101-digit number)

12152419874909433203…92954936811673614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.215 × 10¹⁰⁰(101-digit number)

12152419874909433203…92954936811673614081

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 #534,548

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