Block #2,633,629

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 1:03:24 PM · Difficulty 11.2003 · 4,210,873 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b7f208e43b5f63bd5152d2a3b319145901af570482cb69d7492b88bbc27ae416

View on Chainz ↗

Height

#2,633,629

Difficulty

11.200326

Transactions

Size

619 B

Version

Bits

0b33488c

Nonce

554,635,045

Timestamp

4/28/2018, 1:03:24 PM

Confirmations

4,210,873

Mined by

⛏️ P2SHAe4ceMVE9ScxspLG3qYSssWZWtpiPuKNES

Merkle Root

6f737ede7d47a1bdce0734a9c07939b3bf5c16e14c47a604898c9bf5199bfc27

Transactions (3)

Coinbase4328246c20db0c…a75ea9739b1c64

1 in → 1 out7.9800 XPM110 B

Ae4ceMVE…piPuKNES

8065c6f360e01a…1418b6b4dcf2b0

1 in → 1 out179.9900 XPM192 B

ALd65iyx…WC2oooUw

c19bf2ec097718…b2e8e4c9c6b5a0

1 in → 2 out15229.2697 XPM226 B

AcwFHRsm…TsHiGrsQ AXXGZPK1…cfB9GQPX

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.

1.395 × 10⁹⁷(98-digit number)

13955344579926478438…49399374347500216319

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

1.395 × 10⁹⁷(98-digit number)

13955344579926478438…49399374347500216319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.395 × 10⁹⁷(98-digit number)

13955344579926478438…49399374347500216321

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

2.791 × 10⁹⁷(98-digit number)

27910689159852956877…98798748695000432639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.791 × 10⁹⁷(98-digit number)

27910689159852956877…98798748695000432641

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

5.582 × 10⁹⁷(98-digit number)

55821378319705913754…97597497390000865279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.582 × 10⁹⁷(98-digit number)

55821378319705913754…97597497390000865281

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

1.116 × 10⁹⁸(99-digit number)

11164275663941182750…95194994780001730559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.116 × 10⁹⁸(99-digit number)

11164275663941182750…95194994780001730561

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

2.232 × 10⁹⁸(99-digit number)

22328551327882365501…90389989560003461119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.232 × 10⁹⁸(99-digit number)

22328551327882365501…90389989560003461121

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

4.465 × 10⁹⁸(99-digit number)

44657102655764731003…80779979120006922239

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 #2,633,629

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