Block #2,484,097

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 1/22/2018, 1:42:25 AM · Difficulty 10.9671 · 4,359,320 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4bad868ec54d3ed6ff632e414ad3d3d6ef9fc62dc15ac41a40403b36dc914278

View on Chainz ↗

Height

#2,484,097

Difficulty

10.967139

Transactions

Size

426 B

Version

Bits

0af79665

Nonce

1,484,017,985

Timestamp

1/22/2018, 1:42:25 AM

Confirmations

4,359,320

Mined by

⛏️ P2SHAYjuqfsgZ1qM6pg3oQdkKPMBZqG3BWbMj9

Merkle Root

40c6aa274b5ecd02851064f1a849d525a670d58d694eced0e711cbe31845ca35

Transactions (2)

Coinbasef6ac41f5cd47d2…2f368e0825ce11

1 in → 1 out8.3100 XPM110 B

AYjuqfsg…G3BWbMj9

4a878fb0cd0933…227856da5e33fb

1 in → 2 out9917.3698 XPM227 B

AJaDAB4M…ETHnQd5j AeBAjotr…X2tq83xo

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.

2.305 × 10⁹²(93-digit number)

23054797151589355975…44140761737928276079

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

2.305 × 10⁹²(93-digit number)

23054797151589355975…44140761737928276079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.305 × 10⁹²(93-digit number)

23054797151589355975…44140761737928276081

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

4.610 × 10⁹²(93-digit number)

46109594303178711950…88281523475856552159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.610 × 10⁹²(93-digit number)

46109594303178711950…88281523475856552161

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

9.221 × 10⁹²(93-digit number)

92219188606357423901…76563046951713104319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.221 × 10⁹²(93-digit number)

92219188606357423901…76563046951713104321

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

1.844 × 10⁹³(94-digit number)

18443837721271484780…53126093903426208639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.844 × 10⁹³(94-digit number)

18443837721271484780…53126093903426208641

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

3.688 × 10⁹³(94-digit number)

36887675442542969560…06252187806852417279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.688 × 10⁹³(94-digit number)

36887675442542969560…06252187806852417281

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

7.377 × 10⁹³(94-digit number)

73775350885085939121…12504375613704834559

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 #2,484,097

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