Block #2,389,764

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/22/2017, 2:54:29 AM · Difficulty 10.8733 · 4,427,677 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8ecbe948d769f8b6ae52ea6709b462d918308b81ca30ea8d47c1157c4d5f4e94

View on Chainz ↗

Height

#2,389,764

Difficulty

10.873260

Transactions

Size

721 B

Version

Bits

0adf8dfc

Nonce

18,363,913

Timestamp

11/22/2017, 2:54:29 AM

Confirmations

4,427,677

Mined by

⛏️ P2SHARjbSVoKZEAp4ipesgxGhcR7KUo3h5Zjix

Merkle Root

28b51a74896b91a57963e5a8406200bfd11341463d7a9e7fe4aaf8177ccc2af6

Transactions (2)

Coinbase3fa6c3434e2ead…6e5efc95904e53

1 in → 1 out8.4500 XPM110 B

ARjbSVoK…o3h5Zjix

a86683ee0ea991…9fc4b928d529ca

3 in → 2 out4584.9303 XPM520 B

AXUvfA45…fRtoAx5b ASjkJdks…Wcok8qTL

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.

1.366 × 10⁹⁶(97-digit number)

13667337298626885035…61518586146307768319

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

1.366 × 10⁹⁶(97-digit number)

13667337298626885035…61518586146307768319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.366 × 10⁹⁶(97-digit number)

13667337298626885035…61518586146307768321

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

2.733 × 10⁹⁶(97-digit number)

27334674597253770071…23037172292615536639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.733 × 10⁹⁶(97-digit number)

27334674597253770071…23037172292615536641

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

5.466 × 10⁹⁶(97-digit number)

54669349194507540143…46074344585231073279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.466 × 10⁹⁶(97-digit number)

54669349194507540143…46074344585231073281

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

1.093 × 10⁹⁷(98-digit number)

10933869838901508028…92148689170462146559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.093 × 10⁹⁷(98-digit number)

10933869838901508028…92148689170462146561

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

2.186 × 10⁹⁷(98-digit number)

21867739677803016057…84297378340924293119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.186 × 10⁹⁷(98-digit number)

21867739677803016057…84297378340924293121

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 #2,389,764

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