Block #2,106,577

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/8/2017, 12:23:13 PM · Difficulty 10.8903 · 4,732,246 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6fa602fa3f282d685b4cf2576e0863a98d9607ef2a42a9eefe06e6580ebfb04

View on Chainz ↗

Height

#2,106,577

Difficulty

10.890320

Transactions

Size

1.55 KB

Version

Bits

0ae3ec01

Nonce

333,760,858

Timestamp

5/8/2017, 12:23:13 PM

Confirmations

4,732,246

Mined by

⛏️ P2SHAK8LQwcGgf4umajxyUpNe9VZpkKB8uVfN8

Merkle Root

ddc2ca297006c6a637f375d819d7e18fc350894244f7f6ff64adaa080d42483e

Transactions (4)

Coinbaseeb1c257995ce15…49ff187fc445df

1 in → 1 out8.4500 XPM110 B

AK8LQwcG…KB8uVfN8

fe6f8c4967d8f5…c20dbd2751efa9

1 in → 1 out3.9900 XPM192 B

AbnH38kS…cwGZRciu

3585ec4ed78d0c…471913204c70de

6 in → 2 out121.4832 XPM968 B

AU1awoZc…ap5GRUdT AeAGYg7U…5efhZiSU

0b9625a2eba69b…5bb88844fef5ea

1 in → 2 out3.9900 XPM226 B

AZfrnjXa…iW3cj5BL ALJtqRwj…YQpHohBM

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.

1.295 × 10⁹⁸(99-digit number)

12953208669544234695…81002985784176885759

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

1.295 × 10⁹⁸(99-digit number)

12953208669544234695…81002985784176885759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.295 × 10⁹⁸(99-digit number)

12953208669544234695…81002985784176885761

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

2.590 × 10⁹⁸(99-digit number)

25906417339088469391…62005971568353771519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.590 × 10⁹⁸(99-digit number)

25906417339088469391…62005971568353771521

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

5.181 × 10⁹⁸(99-digit number)

51812834678176938783…24011943136707543039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.181 × 10⁹⁸(99-digit number)

51812834678176938783…24011943136707543041

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

1.036 × 10⁹⁹(100-digit number)

10362566935635387756…48023886273415086079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.036 × 10⁹⁹(100-digit number)

10362566935635387756…48023886273415086081

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

2.072 × 10⁹⁹(100-digit number)

20725133871270775513…96047772546830172159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.072 × 10⁹⁹(100-digit number)

20725133871270775513…96047772546830172161

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 #2,106,577

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