Block #2,157,790

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/12/2017, 3:00:31 PM · Difficulty 10.9053 · 4,659,362 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

38c739b4b82afcdbf0ffc7e355c9f0f58e47ce3831a737d1a27424ae1f7447e5

View on Chainz ↗

Height

#2,157,790

Difficulty

10.905270

Transactions

Size

724 B

Version

Bits

0ae7bfc6

Nonce

1,264,655,324

Timestamp

6/12/2017, 3:00:31 PM

Confirmations

4,659,362

Mined by

⛏️ P2SHAPNVkcEUd5QrgqYojt9ZhYz5Q8urqrX1S5

Merkle Root

d6b98d1784bef1c841f0345337090b7ce0db54de757873afc55df7ed0f110176

Transactions (2)

Coinbase6b16e56aeb934d…ba94444ad1acfa

1 in → 1 out8.4500 XPM109 B

APNVkcEU…urqrX1S5

f72b3dfb55bccb…2bf9b494bb60dc

3 in → 2 out3513.6200 XPM524 B

AZmRZW1G…hEE1AFQa AeGZ1Apc…Z6dDy7qA

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.

9.680 × 10⁹⁷(98-digit number)

96802784226487922133…21985772356266229759

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

9.680 × 10⁹⁷(98-digit number)

96802784226487922133…21985772356266229759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.680 × 10⁹⁷(98-digit number)

96802784226487922133…21985772356266229761

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

1.936 × 10⁹⁸(99-digit number)

19360556845297584426…43971544712532459519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.936 × 10⁹⁸(99-digit number)

19360556845297584426…43971544712532459521

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

3.872 × 10⁹⁸(99-digit number)

38721113690595168853…87943089425064919039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.872 × 10⁹⁸(99-digit number)

38721113690595168853…87943089425064919041

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

7.744 × 10⁹⁸(99-digit number)

77442227381190337707…75886178850129838079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.744 × 10⁹⁸(99-digit number)

77442227381190337707…75886178850129838081

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

1.548 × 10⁹⁹(100-digit number)

15488445476238067541…51772357700259676159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.548 × 10⁹⁹(100-digit number)

15488445476238067541…51772357700259676161

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 #2,157,790

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