Block #2,114,184

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/13/2017, 11:52:18 AM · Difficulty 10.8997 · 4,730,657 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f56fc9b0d57bfe768d1120959cf8acb96f525282885ce3f02e7010364239e629

View on Chainz ↗

Height

#2,114,184

Difficulty

10.899706

Transactions

Size

428 B

Version

Bits

0ae65327

Nonce

1,761,196,562

Timestamp

5/13/2017, 11:52:18 AM

Confirmations

4,730,657

Mined by

⛏️ P2SHAb5EiywBMYb8fA5C7TUe5TSixNidSuQkHt

Merkle Root

12495ef6e654cd9986c4c8210901b7cc53ab63c55f6e37ddd54f29dc67d22c39

Transactions (2)

Coinbasea47f5086a6a567…3a6ede1f6b9573

1 in → 1 out8.4100 XPM110 B

Ab5EiywB…idSuQkHt

b552e89e92dbd4…62272164176ea4

1 in → 2 out185957.0125 XPM227 B

AagJSfV7…f3eFBp3x APMTspTX…fWNRSany

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.

3.464 × 10⁹⁶(97-digit number)

34641005035468862917…70561759837360435199

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

3.464 × 10⁹⁶(97-digit number)

34641005035468862917…70561759837360435199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.464 × 10⁹⁶(97-digit number)

34641005035468862917…70561759837360435201

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

6.928 × 10⁹⁶(97-digit number)

69282010070937725835…41123519674720870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.928 × 10⁹⁶(97-digit number)

69282010070937725835…41123519674720870401

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

1.385 × 10⁹⁷(98-digit number)

13856402014187545167…82247039349441740799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.385 × 10⁹⁷(98-digit number)

13856402014187545167…82247039349441740801

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

2.771 × 10⁹⁷(98-digit number)

27712804028375090334…64494078698883481599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.771 × 10⁹⁷(98-digit number)

27712804028375090334…64494078698883481601

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

5.542 × 10⁹⁷(98-digit number)

55425608056750180668…28988157397766963199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.542 × 10⁹⁷(98-digit number)

55425608056750180668…28988157397766963201

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 #2,114,184

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