Block #2,633,495

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 11:28:55 AM · Difficulty 11.1938 · 4,207,966 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f83cc341bb78b13bc7b089965e6b6d1d11bfeb900119696655a0493c5b99834e

View on Chainz ↗

Height

#2,633,495

Difficulty

11.193763

Transactions

Size

462 B

Version

Bits

0b319a76

Nonce

1,479,422,354

Timestamp

4/28/2018, 11:28:55 AM

Confirmations

4,207,966

Mined by

⛏️ P2SHAbCoKwZZHaYg1F3gfqXEvZkubKtoAAXh2M

Merkle Root

b099937fe43831f0b194a18110e29cf2e4ef786389796260476b8e001ce41fc8

Transactions (2)

Coinbase9158e4372913fe…90b7db3e52f70a

1 in → 1 out7.9800 XPM110 B

AbCoKwZZ…toAAXh2M

2103c490932da1…38cf6b59318da4

1 in → 3 out74.8800 XPM261 B

AS9zqrqs…MMyErqN6 ANvy9K3n…9xwkTv9F AYJF7z3a…ZXfv75UE

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.

1.451 × 10⁹⁷(98-digit number)

14514636164411682815…75116158188988671999

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

1.451 × 10⁹⁷(98-digit number)

14514636164411682815…75116158188988671999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.451 × 10⁹⁷(98-digit number)

14514636164411682815…75116158188988672001

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

2.902 × 10⁹⁷(98-digit number)

29029272328823365631…50232316377977343999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.902 × 10⁹⁷(98-digit number)

29029272328823365631…50232316377977344001

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

5.805 × 10⁹⁷(98-digit number)

58058544657646731263…00464632755954687999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.805 × 10⁹⁷(98-digit number)

58058544657646731263…00464632755954688001

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

1.161 × 10⁹⁸(99-digit number)

11611708931529346252…00929265511909375999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.161 × 10⁹⁸(99-digit number)

11611708931529346252…00929265511909376001

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

2.322 × 10⁹⁸(99-digit number)

23223417863058692505…01858531023818751999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.322 × 10⁹⁸(99-digit number)

23223417863058692505…01858531023818752001

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

4.644 × 10⁹⁸(99-digit number)

46446835726117385010…03717062047637503999

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 #2,633,495

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