Block #2,612,862

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/14/2018, 2:00:49 AM · Difficulty 11.2080 · 4,227,751 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1c4cb3115b0031868c6266494178669e765e2ab93e32052ca514c0987d9bf68e

View on Chainz ↗

Height

#2,612,862

Difficulty

11.208032

Transactions

Size

2.03 KB

Version

Bits

0b35419e

Nonce

309,114,616

Timestamp

4/14/2018, 2:00:49 AM

Confirmations

4,227,751

Mined by

⛏️ P2SHAGVkvzPPRFcMEZf1enNTVYuxXtg87yskBq

Merkle Root

15a693cc5bc573c860e3b880bda016f907d58251f786c54a92d3af1f2a45ee2d

Transactions (5)

Coinbased2f2438be2a8f7…b9a2d0113b2472

1 in → 1 out8.0000 XPM110 B

AGVkvzPP…g87yskBq

84813c5dcc3e19…0cbcb88579d40e

1 in → 2 out7.9100 XPM192 B

AdKhEL4Q…RQS9ZydR AczApyCK…pftvZN1i

6bdf0c663a0fd4…4972bd7ad8dc69

7 in → 2 out40.2371 XPM975 B

AKxyVgfv…3DbH8Mh9 AZp7qc6o…cskCk5jU

9fbc75b388fe03…312246f9f60cc6

2 in → 2 out11.0651 XPM340 B

AUHBKKGB…mR5KpgvJ AeB1Bies…e2NXyAKj

ba80eb61941373…232ad53db4428f

2 in → 2 out4.0408 XPM375 B

AVdRd1AE…9FWjznxr AL5jRkhu…jG4DQ1jD

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.

9.125 × 10⁹⁶(97-digit number)

91253652742827442245…90584260595399731199

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

9.125 × 10⁹⁶(97-digit number)

91253652742827442245…90584260595399731199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.125 × 10⁹⁶(97-digit number)

91253652742827442245…90584260595399731201

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

1.825 × 10⁹⁷(98-digit number)

18250730548565488449…81168521190799462399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.825 × 10⁹⁷(98-digit number)

18250730548565488449…81168521190799462401

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

3.650 × 10⁹⁷(98-digit number)

36501461097130976898…62337042381598924799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.650 × 10⁹⁷(98-digit number)

36501461097130976898…62337042381598924801

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

7.300 × 10⁹⁷(98-digit number)

73002922194261953796…24674084763197849599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.300 × 10⁹⁷(98-digit number)

73002922194261953796…24674084763197849601

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

1.460 × 10⁹⁸(99-digit number)

14600584438852390759…49348169526395699199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.460 × 10⁹⁸(99-digit number)

14600584438852390759…49348169526395699201

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

2.920 × 10⁹⁸(99-digit number)

29201168877704781518…98696339052791398399

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 #2,612,862

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