Block #280,913

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:32:32 PM · Difficulty 9.9757 · 6,544,551 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

800149400a89c96eae283e39df07b2175bb99f795414fdabf348956bdd3bb782

View on Chainz ↗

Height

#280,913

Difficulty

9.975725

Transactions

Size

758 B

Version

Bits

09f9c91b

Nonce

1,078

Timestamp

11/28/2013, 8:32:32 PM

Confirmations

6,544,551

Mined by

⛏️ P2SHAYaTpnoDjg4iRHnzSs6AaFf5TqEJq25nUy

Merkle Root

ba79b202c2e9317b48cc6f056dec0a5b1d93786404a06e4355cf41a732dff505

Transactions (2)

Coinbase18d18e362ff346…15bd066c0e46a5

1 in → 2 out10.0400 XPM141 B

AYaTpnoD…EJq25nUy AHsw4d6U…EnM8UXNZ

5f455bb2d7a9c8…973e1575cf1a2f

3 in → 2 out815.9235 XPM524 B

AdQWpkHE…4HrnNMBe AHCo7xYs…dvyvf2BG

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.

5.271 × 10¹⁰¹(102-digit number)

52713700481308358293…81447291443412485119

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

5.271 × 10¹⁰¹(102-digit number)

52713700481308358293…81447291443412485119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.271 × 10¹⁰¹(102-digit number)

52713700481308358293…81447291443412485121

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

1.054 × 10¹⁰²(103-digit number)

10542740096261671658…62894582886824970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.054 × 10¹⁰²(103-digit number)

10542740096261671658…62894582886824970241

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

2.108 × 10¹⁰²(103-digit number)

21085480192523343317…25789165773649940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.108 × 10¹⁰²(103-digit number)

21085480192523343317…25789165773649940481

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

4.217 × 10¹⁰²(103-digit number)

42170960385046686634…51578331547299880959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.217 × 10¹⁰²(103-digit number)

42170960385046686634…51578331547299880961

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

8.434 × 10¹⁰²(103-digit number)

84341920770093373269…03156663094599761919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.434 × 10¹⁰²(103-digit number)

84341920770093373269…03156663094599761921

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 #280,913

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