Block #2,336,610

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/14/2017, 2:50:13 PM · Difficulty 10.9183 · 4,504,324 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a9a1459ea1b28ddb15f4a72d47e0071af2f0befa3511e452ba9257745099c337

View on Chainz ↗

Height

#2,336,610

Difficulty

10.918266

Transactions

Size

808 B

Version

Bits

0aeb1375

Nonce

593,448,613

Timestamp

10/14/2017, 2:50:13 PM

Confirmations

4,504,324

Mined by

⛏️ P2SHAV18HsCkEwKy9kFB7AvBwx33GZwDULc68Z

Merkle Root

9560c4cd58442d24310e7ef22ed8c654b234ff567b4257339092e8593a671e44

Transactions (4)

Coinbase66a1345aca8624…dd3d8dc494e68f

1 in → 1 out8.4100 XPM109 B

AV18HsCk…wDULc68Z

247bd9d8978b62…89da382a83949b

1 in → 2 out2589.1272 XPM226 B

Aajkp9LH…oMnkP9mc AVpwAULp…EjU8ws2i

5d63f977cf292a…06a736c460fcd1

1 in → 2 out8.3800 XPM192 B

AJKhs9Jh…coc8bj46 AKatK3j1…WGrp4VZL

a76537f49ce351…ad672c5aa9fe19

1 in → 2 out8.3600 XPM192 B

AJMrMUVA…XLVBXChy ALUJ2a1f…Ltkvvr8Q

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.

3.745 × 10⁹²(93-digit number)

37453935852093466706…58039680105597640959

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

3.745 × 10⁹²(93-digit number)

37453935852093466706…58039680105597640959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.745 × 10⁹²(93-digit number)

37453935852093466706…58039680105597640961

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

7.490 × 10⁹²(93-digit number)

74907871704186933412…16079360211195281919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.490 × 10⁹²(93-digit number)

74907871704186933412…16079360211195281921

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

1.498 × 10⁹³(94-digit number)

14981574340837386682…32158720422390563839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.498 × 10⁹³(94-digit number)

14981574340837386682…32158720422390563841

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

2.996 × 10⁹³(94-digit number)

29963148681674773365…64317440844781127679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.996 × 10⁹³(94-digit number)

29963148681674773365…64317440844781127681

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

5.992 × 10⁹³(94-digit number)

59926297363349546730…28634881689562255359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.992 × 10⁹³(94-digit number)

59926297363349546730…28634881689562255361

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 #2,336,610

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