Block #2,176,616

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/25/2017, 2:43:31 AM · Difficulty 10.9203 · 4,637,266 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4a81dac5b40e0995bcfbbd852602092565e7d5035b0c34ca5f661c894e72b0ec

View on Chainz ↗

Height

#2,176,616

Difficulty

10.920346

Transactions

Size

755 B

Version

Bits

0aeb9bd0

Nonce

108,386,906

Timestamp

6/25/2017, 2:43:31 AM

Confirmations

4,637,266

Mined by

⛏️ P2SHALRiv93X2RbSeENdDne8msihBiZvNaX8qX

Merkle Root

89679fe9482e2f3f4447956dafa7a794805f796199248277d90b1aecb8a8898d

Transactions (2)

Coinbasec7075544a5549d…4db3331e7ad4d3

1 in → 1 out8.3800 XPM109 B

ALRiv93X…ZvNaX8qX

35348517298319…c9317ea63a39ea

3 in → 3 out1789.6386 XPM555 B

AXDFfBoh…2WiskE5b AVB8Kqgj…zUanL8Tf ALjVzEH6…ZtoUaFFi

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.

4.989 × 10⁹⁷(98-digit number)

49890895664545044261…61807936677927403519

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

4.989 × 10⁹⁷(98-digit number)

49890895664545044261…61807936677927403519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.989 × 10⁹⁷(98-digit number)

49890895664545044261…61807936677927403521

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

9.978 × 10⁹⁷(98-digit number)

99781791329090088523…23615873355854807039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.978 × 10⁹⁷(98-digit number)

99781791329090088523…23615873355854807041

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

1.995 × 10⁹⁸(99-digit number)

19956358265818017704…47231746711709614079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.995 × 10⁹⁸(99-digit number)

19956358265818017704…47231746711709614081

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

3.991 × 10⁹⁸(99-digit number)

39912716531636035409…94463493423419228159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.991 × 10⁹⁸(99-digit number)

39912716531636035409…94463493423419228161

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

7.982 × 10⁹⁸(99-digit number)

79825433063272070819…88926986846838456319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.982 × 10⁹⁸(99-digit number)

79825433063272070819…88926986846838456321

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 #2,176,616

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