Block #2,314,420

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/29/2017, 3:11:46 PM · Difficulty 10.9069 · 4,512,716 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

62bbcb9d28bb9871af1b3eb0753a77c31f01a32a85da6e120590c8ce3ebdd5a6

View on Chainz ↗

Height

#2,314,420

Difficulty

10.906908

Transactions

Size

1.33 KB

Version

Bits

0ae82b20

Nonce

145,941,547

Timestamp

9/29/2017, 3:11:46 PM

Confirmations

4,512,716

Mined by

⛏️ P2SHAYJu2DnkyNVsHkoKQNgm4FyH3QEBkbiK5r

Merkle Root

4aaff942f16a670d053c30f59de129795a32138f3cc09fe0e2cb57674d99951a

Transactions (5)

Coinbase5277c60777c361…832684afccb7b5

1 in → 1 out8.4300 XPM109 B

AYJu2Dnk…EBkbiK5r

35c1130311afdf…9ecd6a95439ca1

3 in → 1 out1799.9900 XPM487 B

AcxhUhX6…N8N8w2tm

4588d8a45d34c0…131513c7767a04

1 in → 2 out4.1678 XPM227 B

AYUY6QBZ…nstBEWCQ AckeZrK6…PJ9R155S

9c242f1c97feff…bb3b7a34094330

1 in → 2 out2.2705 XPM225 B

AJn6Nx8e…eMgJCPNY AQBd5saN…gzPybU6u

b2e789ae7a4b50…9dc36f8dc9b444

1 in → 2 out1.3614 XPM226 B

AH6Evz47…XcsNigfb AXAbVAXM…tAjzQQxM

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.

5.284 × 10⁹¹(92-digit number)

52845442075182984742…58822809268317566559

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

5.284 × 10⁹¹(92-digit number)

52845442075182984742…58822809268317566559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.284 × 10⁹¹(92-digit number)

52845442075182984742…58822809268317566561

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

1.056 × 10⁹²(93-digit number)

10569088415036596948…17645618536635133119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.056 × 10⁹²(93-digit number)

10569088415036596948…17645618536635133121

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

2.113 × 10⁹²(93-digit number)

21138176830073193897…35291237073270266239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.113 × 10⁹²(93-digit number)

21138176830073193897…35291237073270266241

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

4.227 × 10⁹²(93-digit number)

42276353660146387794…70582474146540532479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.227 × 10⁹²(93-digit number)

42276353660146387794…70582474146540532481

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

8.455 × 10⁹²(93-digit number)

84552707320292775588…41164948293081064959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.455 × 10⁹²(93-digit number)

84552707320292775588…41164948293081064961

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 #2,314,420

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