Block #280,908

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/28/2013, 8:30:37 PM · Difficulty 9.9757 · 6,527,511 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

572951408bd777ef07c302417920ce851cda86e4eef64d293332bb8747ad259c

View on Chainz ↗

Height

#280,908

Difficulty

9.975721

Transactions

Size

1003 B

Version

Bits

09f9c8d3

Nonce

8,862

Timestamp

11/28/2013, 8:30:37 PM

Confirmations

6,527,511

Mined by

⛏️ LIaRAc5fJQHGYB6NrBP8Ud1pcwESC3q84K4Avs

Merkle Root

83a51dce5b7b19b136f80dee541d1dcb2e8080a0570e889cedd0291706d358bf

Transactions (1)

Coinbase83a51dce5b7b19…d0291706d358bf

1 in → 25 out10.0296 XPM913 B

Ac5fJQHG…q84K4Avs ARyioPoT…UiofHnMr AWNm5iN2…RrkMw1vi AK3vz3dH…9NvorskL AJiNZZJs…BiqAhyiP

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.

1.971 × 10⁹⁵(96-digit number)

19712764776144213840…86043611676499799999

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

1.971 × 10⁹⁵(96-digit number)

19712764776144213840…86043611676499799999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.971 × 10⁹⁵(96-digit number)

19712764776144213840…86043611676499800001

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

3.942 × 10⁹⁵(96-digit number)

39425529552288427680…72087223352999599999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.942 × 10⁹⁵(96-digit number)

39425529552288427680…72087223352999600001

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

7.885 × 10⁹⁵(96-digit number)

78851059104576855361…44174446705999199999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.885 × 10⁹⁵(96-digit number)

78851059104576855361…44174446705999200001

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

1.577 × 10⁹⁶(97-digit number)

15770211820915371072…88348893411998399999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.577 × 10⁹⁶(97-digit number)

15770211820915371072…88348893411998400001

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

3.154 × 10⁹⁶(97-digit number)

31540423641830742144…76697786823996799999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.154 × 10⁹⁶(97-digit number)

31540423641830742144…76697786823996800001

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

6.308 × 10⁹⁶(97-digit number)

63080847283661484289…53395573647993599999

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #280,908

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