Block #460,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/26/2014, 2:42:33 AM · Difficulty 10.4163 · 6,338,711 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

45efebb9ddd5fcca7811e6e038f661866601420d25db520d24508a37ee5724d0

View on Chainz ↗

Height

#460,557

Difficulty

10.416287

Transactions

Size

2.02 KB

Version

Bits

0a6a91ca

Nonce

50,921

Timestamp

3/26/2014, 2:42:33 AM

Confirmations

6,338,711

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

14e2f7804c8fc4d992243f0058cf71a6873ec2a84501a7441ed4d10acaaa709e

Transactions (4)

Coinbase71790e4973d818…c829c3a8c685c8

1 in → 1 out9.2400 XPM110 B

AeKNrjNj…1NEq95Ta

35d00947f11ad4…14d595e965bfbf

1 in → 2 out4.9900 XPM226 B

AR8Fzm9z…bzBApM9q ANU1wozV…SN4aeYGv

9fa2086aa60698…deb9b5debc795f

2 in → 2 out3.9900 XPM373 B

AJGeFYcB…oMF9jKht ASLecf1k…VWUjWzE7

3d2932da0920b9…4b49b024999e09

8 in → 2 out26.6450 XPM1.23 KB

AZUQETZh…Y1CVGBus AG3M5q6Y…NNP4pkjk

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.

2.126 × 10¹⁰¹(102-digit number)

21267273788785086187…16057661667437285759

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

2.126 × 10¹⁰¹(102-digit number)

21267273788785086187…16057661667437285759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.126 × 10¹⁰¹(102-digit number)

21267273788785086187…16057661667437285761

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

4.253 × 10¹⁰¹(102-digit number)

42534547577570172375…32115323334874571519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.253 × 10¹⁰¹(102-digit number)

42534547577570172375…32115323334874571521

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

8.506 × 10¹⁰¹(102-digit number)

85069095155140344750…64230646669749143039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.506 × 10¹⁰¹(102-digit number)

85069095155140344750…64230646669749143041

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

1.701 × 10¹⁰²(103-digit number)

17013819031028068950…28461293339498286079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.701 × 10¹⁰²(103-digit number)

17013819031028068950…28461293339498286081

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

3.402 × 10¹⁰²(103-digit number)

34027638062056137900…56922586678996572159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.402 × 10¹⁰²(103-digit number)

34027638062056137900…56922586678996572161

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

6.805 × 10¹⁰²(103-digit number)

68055276124112275800…13845173357993144319

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