Block #2,672,350

TWNLength 12★★★★☆

Bi-Twin Chain · Discovered 5/22/2018, 2:04:57 AM · Difficulty 11.6939 · 4,160,643 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fe776fc9cc7a9e9882b4be91472866f446d00e99381067ca3ae2b9e712328d0

View on Chainz ↗

Height

#2,672,350

Difficulty

11.693950

Transactions

Size

1.56 KB

Version

Bits

0bb1a6ae

Nonce

969,973,312

Timestamp

5/22/2018, 2:04:57 AM

Confirmations

4,160,643

Mined by

⛏️ P2SHAR2ow7h87RhxjfEWxdYvJSvfozikwfHcNm

Merkle Root

3daa4a728e025545bb381f26cb0ed6395eba43cca0392c713146f940c1f76f1f

Transactions (5)

Coinbaseceb8d213fd3083…196ed18d180992

1 in → 1 out7.3400 XPM110 B

AR2ow7h8…ikwfHcNm

dd06d89c104aea…58dfc73adb5cd0

2 in → 2 out11.9400 XPM340 B

AanDRiDY…X9rpqpgr AbG36wjz…2qEevhm1

03d7e437c6690a…5f2b4dc5aa6016

2 in → 2 out11.9500 XPM340 B

APVKWthF…PMMxwRoz AYP9krg8…fReKRqHx

c542c2bdfb93fa…a51b81f3e05a0b

3 in → 2 out10.4500 XPM489 B

AHitKfX9…CAUCXREU ATEy9cxL…LgviB6pF

ae7eb408c230e0…5a9a51c3c13c7c

1 in → 2 out1.9906 XPM226 B

AMpd1S2A…AbwMKvSY AKPhZnKP…wzQ58nni

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.

1.061 × 10⁹⁶(97-digit number)

10610568110126017403…74955797671248184319

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

1.061 × 10⁹⁶(97-digit number)

10610568110126017403…74955797671248184319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.061 × 10⁹⁶(97-digit number)

10610568110126017403…74955797671248184321

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

2.122 × 10⁹⁶(97-digit number)

21221136220252034807…49911595342496368639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.122 × 10⁹⁶(97-digit number)

21221136220252034807…49911595342496368641

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

4.244 × 10⁹⁶(97-digit number)

42442272440504069614…99823190684992737279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.244 × 10⁹⁶(97-digit number)

42442272440504069614…99823190684992737281

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

8.488 × 10⁹⁶(97-digit number)

84884544881008139228…99646381369985474559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.488 × 10⁹⁶(97-digit number)

84884544881008139228…99646381369985474561

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

1.697 × 10⁹⁷(98-digit number)

16976908976201627845…99292762739970949119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.697 × 10⁹⁷(98-digit number)

16976908976201627845…99292762739970949121

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

3.395 × 10⁹⁷(98-digit number)

33953817952403255691…98585525479941898239

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

3.395 × 10⁹⁷(98-digit number)

33953817952403255691…98585525479941898241

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 12 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

ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

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 #2,672,350

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