Block #2,270,514

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 8/27/2017, 4:04:54 PM · Difficulty 10.9529 · 4,560,379 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8a0a3188d5bded1ca9498067a07fa154f9d3281e356c55702bca17d16cd9d02b

View on Chainz ↗

Height

#2,270,514

Difficulty

10.952905

Transactions

Size

1.36 KB

Version

Bits

0af3f193

Nonce

497,498,351

Timestamp

8/27/2017, 4:04:54 PM

Confirmations

4,560,379

Mined by

⛏️ P2SHAc3dTih8ciGgUAvkSSTyP4gs7e6cPaTgXX

Merkle Root

e7e2021be4ab9377c63059603488d26546a78035de314adde45c1f893d97275e

Transactions (3)

Coinbase03bc55e2731d58…e73446cfbb3b64

1 in → 1 out8.3500 XPM109 B

Ac3dTih8…6cPaTgXX

beb3bb95f7a357…1ff3845d1349a8

2 in → 2 out432.2144 XPM375 B

Af4Uuyr4…ru1KiSX1 ANUNBsPw…gsu2VPVU

976dc172940dca…a3809f5304ebff

5 in → 2 out1005.9900 XPM819 B

AbzkNz6M…S7RjG6Fg ANY5KTzv…EzpB9MEw

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.

2.581 × 10⁹⁵(96-digit number)

25818175708196353643…15810864180605230079

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

2.581 × 10⁹⁵(96-digit number)

25818175708196353643…15810864180605230079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.581 × 10⁹⁵(96-digit number)

25818175708196353643…15810864180605230081

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

5.163 × 10⁹⁵(96-digit number)

51636351416392707286…31621728361210460159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.163 × 10⁹⁵(96-digit number)

51636351416392707286…31621728361210460161

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

1.032 × 10⁹⁶(97-digit number)

10327270283278541457…63243456722420920319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.032 × 10⁹⁶(97-digit number)

10327270283278541457…63243456722420920321

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

2.065 × 10⁹⁶(97-digit number)

20654540566557082914…26486913444841840639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.065 × 10⁹⁶(97-digit number)

20654540566557082914…26486913444841840641

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

4.130 × 10⁹⁶(97-digit number)

41309081133114165829…52973826889683681279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.130 × 10⁹⁶(97-digit number)

41309081133114165829…52973826889683681281

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 #2,270,514

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