Block #2,214,065

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 7/19/2017, 11:31:00 PM · Difficulty 10.9437 · 4,628,428 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e67044d62fb03f0b1462e09b402b5cc355038c52d7fa0ab85ccd973c5a7bb0ca

View on Chainz ↗

Height

#2,214,065

Difficulty

10.943679

Transactions

Size

427 B

Version

Bits

0af194f3

Nonce

456,813,630

Timestamp

7/19/2017, 11:31:00 PM

Confirmations

4,628,428

Mined by

⛏️ P2SHAcDQF3VPc6ejKa9Lk3sg3HekCKyfWJ8PMA

Merkle Root

12a7b7555c44a1a6cfbadfe6d2d5b4a148cedfc5917241c5cce8b402fa31f193

Transactions (2)

Coinbase329bd3820972cb…02fad58c8a21d8

1 in → 1 out8.3500 XPM110 B

AcDQF3VP…yfWJ8PMA

9fecb969a2c977…0d6df52a673d3b

1 in → 2 out796.2104 XPM226 B

AQmvnLRh…dew3bJDZ AVcCWawq…ab8VQHsZ

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.

9.849 × 10⁹⁷(98-digit number)

98490802108220833206…49985761682929745919

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

9.849 × 10⁹⁷(98-digit number)

98490802108220833206…49985761682929745919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.849 × 10⁹⁷(98-digit number)

98490802108220833206…49985761682929745921

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

1.969 × 10⁹⁸(99-digit number)

19698160421644166641…99971523365859491839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.969 × 10⁹⁸(99-digit number)

19698160421644166641…99971523365859491841

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

3.939 × 10⁹⁸(99-digit number)

39396320843288333282…99943046731718983679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.939 × 10⁹⁸(99-digit number)

39396320843288333282…99943046731718983681

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

7.879 × 10⁹⁸(99-digit number)

78792641686576666565…99886093463437967359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.879 × 10⁹⁸(99-digit number)

78792641686576666565…99886093463437967361

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

1.575 × 10⁹⁹(100-digit number)

15758528337315333313…99772186926875934719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.575 × 10⁹⁹(100-digit number)

15758528337315333313…99772186926875934721

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 #2,214,065

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