Block #2,099,719

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2017, 4:40:08 PM · Difficulty 10.8562 · 4,725,662 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e2b3faa734c02193007f1fb5d503564e50418c141d91d2db99f3e6ccbd8bacaf

View on Chainz ↗

Height

#2,099,719

Difficulty

10.856245

Transactions

Size

16.32 KB

Version

Bits

0adb32e0

Nonce

170,167,197

Timestamp

5/4/2017, 4:40:08 PM

Confirmations

4,725,662

Mined by

⛏️ P2SHAUFgAUTYT6oEPvDgqo1VJBxqytPwkpxUD5

Merkle Root

029bb4d635e13f9b509eb4b2ad5d94f7ad97773a630b548fd05b3eed5b780785

Transactions (2)

Coinbase6f7088f3e6f1e4…26a38aca40d67b

1 in → 1 out8.6400 XPM109 B

AUFgAUTY…PwkpxUD5

0e29903b6ea785…161a5c4bb0c3c8

111 in → 2 out1441.3878 XPM16.12 KB

Adufj5hW…X6QSwoFe AMRycWoF…13hkF5ou

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.

1.170 × 10⁹⁸(99-digit number)

11700395324991584110…35258539680302366719

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

1.170 × 10⁹⁸(99-digit number)

11700395324991584110…35258539680302366719

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.170 × 10⁹⁸(99-digit number)

11700395324991584110…35258539680302366721

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

2.340 × 10⁹⁸(99-digit number)

23400790649983168221…70517079360604733439

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.340 × 10⁹⁸(99-digit number)

23400790649983168221…70517079360604733441

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

4.680 × 10⁹⁸(99-digit number)

46801581299966336443…41034158721209466879

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.680 × 10⁹⁸(99-digit number)

46801581299966336443…41034158721209466881

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

9.360 × 10⁹⁸(99-digit number)

93603162599932672887…82068317442418933759

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.360 × 10⁹⁸(99-digit number)

93603162599932672887…82068317442418933761

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

1.872 × 10⁹⁹(100-digit number)

18720632519986534577…64136634884837867519

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.872 × 10⁹⁹(100-digit number)

18720632519986534577…64136634884837867521

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 #2,099,719

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