Block #280,469

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/28/2013, 4:50:30 PM · Difficulty 9.9746 · 6,537,300 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

420ee5a3cc09a93eecc52fa2a93a770b58de901fca32fc1d678ebb782b8a1bac

View on Chainz ↗

Height

#280,469

Difficulty

9.974624

Transactions

Size

198 B

Version

Bits

09f980f9

Nonce

30,411

Timestamp

11/28/2013, 4:50:30 PM

Confirmations

6,537,300

Mined by

⛏️ P2SHAR2xarUCbxAqiuA4pD5oU948UXKfF78gk7

Merkle Root

f86c18a9431ff4472641bac581a18e6800cd6c3f8cc8f443d702ca90b68ec3aa

Transactions (1)

Coinbasef86c18a9431ff4…02ca90b68ec3aa

1 in → 1 out10.0400 XPM109 B

AR2xarUC…KfF78gk7

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.

3.033 × 10⁹³(94-digit number)

30330537737784494781…53042848946182450559

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

3.033 × 10⁹³(94-digit number)

30330537737784494781…53042848946182450559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.033 × 10⁹³(94-digit number)

30330537737784494781…53042848946182450561

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

6.066 × 10⁹³(94-digit number)

60661075475568989562…06085697892364901119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.066 × 10⁹³(94-digit number)

60661075475568989562…06085697892364901121

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

1.213 × 10⁹⁴(95-digit number)

12132215095113797912…12171395784729802239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.213 × 10⁹⁴(95-digit number)

12132215095113797912…12171395784729802241

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

2.426 × 10⁹⁴(95-digit number)

24264430190227595824…24342791569459604479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.426 × 10⁹⁴(95-digit number)

24264430190227595824…24342791569459604481

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

4.852 × 10⁹⁴(95-digit number)

48528860380455191649…48685583138919208959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.852 × 10⁹⁴(95-digit number)

48528860380455191649…48685583138919208961

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 #280,469

Cookie Preferences