Block #453,833

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/21/2014, 1:29:25 PM · Difficulty 10.3912 · 6,345,452 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

08bd294086594fd95fa299b82ed2f23822eb014a3f6c73523b8631ccfe88d695

View on Chainz ↗

Height

#453,833

Difficulty

10.391231

Transactions

Size

1.22 KB

Version

Bits

0a6427bf

Nonce

48,028

Timestamp

3/21/2014, 1:29:25 PM

Confirmations

6,345,452

Mined by

⛏️ P2SHAbpudCNgSoPEJgJXw7EQb9bG1jpfoNjPAX

Merkle Root

90f4a1a65113fce0b71aafbb81660bf02fd32e1ec8ddd99d8585425cf2a28fd7

Transactions (5)

Coinbase91bbeb17bf4ba5…b09f04d8c56fb0

1 in → 1 out9.2900 XPM110 B

AbpudCNg…pfoNjPAX

28f40c0adbf908…35ded96d7dfadc

1 in → 2 out9.2700 XPM225 B

AcQfxVUD…vQnNph4X AYNs1Zmu…DLmwD4rv

060f791bd64841…7e3d1f34af307c

2 in → 2 out10.4920 XPM373 B

AJJu16ii…1zZTWnqc AZfrsETj…eFih1ZSS

442713d8db0d29…8fd44aa2045c0e

1 in → 2 out4.7155 XPM226 B

AYFxzicp…jeAdgy2P AZeSKrFc…AgDqLBgN

c393eb742f36be…073ff1b1e027df

1 in → 2 out4.2089 XPM226 B

ALVMsfjq…GPnskiJz AGSaafUV…fiRB5Qoe

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.

8.802 × 10⁹⁸(99-digit number)

88023753505347389681…62447404060182126559

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

8.802 × 10⁹⁸(99-digit number)

88023753505347389681…62447404060182126559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.802 × 10⁹⁸(99-digit number)

88023753505347389681…62447404060182126561

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

1.760 × 10⁹⁹(100-digit number)

17604750701069477936…24894808120364253119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.760 × 10⁹⁹(100-digit number)

17604750701069477936…24894808120364253121

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

3.520 × 10⁹⁹(100-digit number)

35209501402138955872…49789616240728506239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.520 × 10⁹⁹(100-digit number)

35209501402138955872…49789616240728506241

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

7.041 × 10⁹⁹(100-digit number)

70419002804277911745…99579232481457012479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.041 × 10⁹⁹(100-digit number)

70419002804277911745…99579232481457012481

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

1.408 × 10¹⁰⁰(101-digit number)

14083800560855582349…99158464962914024959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.408 × 10¹⁰⁰(101-digit number)

14083800560855582349…99158464962914024961

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

2.816 × 10¹⁰⁰(101-digit number)

28167601121711164698…98316929925828049919

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