Block #1,086,459

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/2/2015, 6:51:31 AM · Difficulty 10.7519 · 5,731,360 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ec03ab7c6d105e2aeb171b7ac2c44642c22eb44fc8f60c802acef2d72acaed82

View on Chainz ↗

Height

#1,086,459

Difficulty

10.751860

Transactions

Size

1.85 KB

Version

Bits

0ac079ea

Nonce

112,354

Timestamp

6/2/2015, 6:51:31 AM

Confirmations

5,731,360

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

a8b4b4fa8cb7bcbfe2caa70f7eee24a43cf5ff49c2856e3555daa946e2c21f91

Transactions (2)

Coinbase973688ad0d7785…50d719f3e910e8

1 in → 1 out8.6600 XPM116 B

ANSXnLY2…Sd25TjkD

64bc3f456cec95…3bd3508f167573

1 in → 45 out36.2041 XPM1.65 KB

AejcsRHy…X15pK4mH AJH6jczt…3R5K3Udf AWj9dfz4…P9Y9NYrJ ATPTxPp2…uXj9F1fT ALiF66vS…kpnKwvwV

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.

2.811 × 10⁹⁶(97-digit number)

28114956277917198018…21334912494752915099

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

2.811 × 10⁹⁶(97-digit number)

28114956277917198018…21334912494752915099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.811 × 10⁹⁶(97-digit number)

28114956277917198018…21334912494752915101

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

5.622 × 10⁹⁶(97-digit number)

56229912555834396036…42669824989505830199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.622 × 10⁹⁶(97-digit number)

56229912555834396036…42669824989505830201

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

1.124 × 10⁹⁷(98-digit number)

11245982511166879207…85339649979011660399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.124 × 10⁹⁷(98-digit number)

11245982511166879207…85339649979011660401

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

2.249 × 10⁹⁷(98-digit number)

22491965022333758414…70679299958023320799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.249 × 10⁹⁷(98-digit number)

22491965022333758414…70679299958023320801

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

4.498 × 10⁹⁷(98-digit number)

44983930044667516829…41358599916046641599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.498 × 10⁹⁷(98-digit number)

44983930044667516829…41358599916046641601

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 #1,086,459

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