Block #1,545,548

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/17/2016, 1:50:13 PM · Difficulty 10.6578 · 5,298,212 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

23a5069b06bdef638695e8ed1bfb3cfd1cf4b419cc071a4d90b9bc8192b5216b

View on Chainz ↗

Height

#1,545,548

Difficulty

10.657814

Transactions

Size

11.47 KB

Version

Bits

0aa8667e

Nonce

273,143,301

Timestamp

4/17/2016, 1:50:13 PM

Confirmations

5,298,212

Mined by

⛏️ P2SHASvF7S9ZYUszrtKa8wQbwx8SPue8ckg9Jt

Merkle Root

39414961da5fa42f778484891aa78ffce02209bc33b9216abe72021f0a7b0e05

Transactions (3)

Coinbase43d314f50968ea…af6d3347244be4

1 in → 1 out9.0000 XPM110 B

ASvF7S9Z…e8ckg9Jt

215890ea283da8…4b68dc00ee6bcb

76 in → 2 out182.4898 XPM11.06 KB

AZ2QkXK9…dVd6fkjE AHNkwmbJ…EUxEmniY

80dd830ebde6ad…aa580fa0e91fe0

1 in → 2 out24.4647 XPM227 B

ARSGwfvq…RdvnptaP AHRDMacP…j2APw6FK

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.

2.930 × 10⁹⁵(96-digit number)

29308130771596714793…88540277764512729679

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

2.930 × 10⁹⁵(96-digit number)

29308130771596714793…88540277764512729679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.930 × 10⁹⁵(96-digit number)

29308130771596714793…88540277764512729681

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

5.861 × 10⁹⁵(96-digit number)

58616261543193429587…77080555529025459359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.861 × 10⁹⁵(96-digit number)

58616261543193429587…77080555529025459361

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

1.172 × 10⁹⁶(97-digit number)

11723252308638685917…54161111058050918719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.172 × 10⁹⁶(97-digit number)

11723252308638685917…54161111058050918721

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

2.344 × 10⁹⁶(97-digit number)

23446504617277371834…08322222116101837439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.344 × 10⁹⁶(97-digit number)

23446504617277371834…08322222116101837441

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

4.689 × 10⁹⁶(97-digit number)

46893009234554743669…16644444232203674879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.689 × 10⁹⁶(97-digit number)

46893009234554743669…16644444232203674881

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 #1,545,548

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