Block #2,940,224

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/26/2018, 4:56:05 PM · Difficulty 11.3742 · 3,893,570 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

acb6fe71dc82e68f3229d32c290dce5cd1c95347e935740f9932b0771d847bf2

View on Chainz ↗

Height

#2,940,224

Difficulty

11.374230

Transactions

Size

1020 B

Version

Bits

0b5fcd8b

Nonce

372,062,486

Timestamp

11/26/2018, 4:56:05 PM

Confirmations

3,893,570

Mined by

⛏️ P2SHAUMQRepmQQz6L5K9d1Muaf8ABjtAfKmdW1

Merkle Root

9b5043c99d25db1250bc77cb60b9b588c317dfc75bffc654354b2f68b09bf8d6

Transactions (2)

Coinbase3b3c266eb17325…8d27f64d792b02

1 in → 1 out7.7300 XPM110 B

AUMQRepm…tAfKmdW1

671ed2a38c513c…80a909b4b404b6

5 in → 2 out327.2487 XPM820 B

ARTGxeAc…WmRAvHDa AbRABbc8…2TVvdp8s

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.

6.331 × 10⁹⁴(95-digit number)

63317808060388235113…02573444900310796799

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

6.331 × 10⁹⁴(95-digit number)

63317808060388235113…02573444900310796799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.331 × 10⁹⁴(95-digit number)

63317808060388235113…02573444900310796801

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

1.266 × 10⁹⁵(96-digit number)

12663561612077647022…05146889800621593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.266 × 10⁹⁵(96-digit number)

12663561612077647022…05146889800621593601

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

2.532 × 10⁹⁵(96-digit number)

25327123224155294045…10293779601243187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.532 × 10⁹⁵(96-digit number)

25327123224155294045…10293779601243187201

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

5.065 × 10⁹⁵(96-digit number)

50654246448310588090…20587559202486374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.065 × 10⁹⁵(96-digit number)

50654246448310588090…20587559202486374401

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

1.013 × 10⁹⁶(97-digit number)

10130849289662117618…41175118404972748799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.013 × 10⁹⁶(97-digit number)

10130849289662117618…41175118404972748801

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

2.026 × 10⁹⁶(97-digit number)

20261698579324235236…82350236809945497599

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,940,224

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