Block #2,130,983

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/24/2017, 6:59:15 PM · Difficulty 10.9103 · 4,707,314 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3078712ae7e6d2f55c64365cba847ff7d9a8d3793ef0c4ce4e82d6dd219d0906

View on Chainz ↗

Height

#2,130,983

Difficulty

10.910272

Transactions

Size

869 B

Version

Bits

0ae90792

Nonce

9,331,103

Timestamp

5/24/2017, 6:59:15 PM

Confirmations

4,707,314

Mined by

⛏️ P2SHAGtz9Fbb76hGjndsEEadLTHdzZ3MrqJBXt

Merkle Root

04f1de644989176af7b31b8999d2185d0cbd22e5b2022b53199a33e60304e8a0

Transactions (2)

Coinbase9b928ea789f5ba…6ee0db686b2c90

1 in → 1 out8.4000 XPM109 B

AGtz9Fbb…3MrqJBXt

70608e0e7389d8…b722b2b3332534

4 in → 2 out15.8225 XPM668 B

AZGHDMdT…dYpBoxtr AKGxoSP8…8oH3hVLd

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.

3.737 × 10⁹⁸(99-digit number)

37371837010839721595…66477550482851430399

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

3.737 × 10⁹⁸(99-digit number)

37371837010839721595…66477550482851430399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.737 × 10⁹⁸(99-digit number)

37371837010839721595…66477550482851430401

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

7.474 × 10⁹⁸(99-digit number)

74743674021679443191…32955100965702860799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.474 × 10⁹⁸(99-digit number)

74743674021679443191…32955100965702860801

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

1.494 × 10⁹⁹(100-digit number)

14948734804335888638…65910201931405721599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.494 × 10⁹⁹(100-digit number)

14948734804335888638…65910201931405721601

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

2.989 × 10⁹⁹(100-digit number)

29897469608671777276…31820403862811443199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.989 × 10⁹⁹(100-digit number)

29897469608671777276…31820403862811443201

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

5.979 × 10⁹⁹(100-digit number)

59794939217343554553…63640807725622886399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.979 × 10⁹⁹(100-digit number)

59794939217343554553…63640807725622886401

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 #2,130,983

Cookie Preferences