Block #2,862,736

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 10/1/2018, 2:07:23 PM · Difficulty 11.6740 · 3,981,750 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5c0957c5a62451537c05f9c0b5f6f5f82d799e92c842a94d956ff2d172ea2e21

View on Chainz ↗

Height

#2,862,736

Difficulty

11.674049

Transactions

Size

1.16 KB

Version

Bits

0bac8e7c

Nonce

1,076,923,357

Timestamp

10/1/2018, 2:07:23 PM

Confirmations

3,981,750

Mined by

⛏️ P2SHAGtjVNkzv6ArvZGzhvjSe5uDcZZ6kHj1Lb

Merkle Root

941b2b9ce9f589aeab621cd3fb1dfbcb14e879e81e219c4dece4748b464e207c

Transactions (4)

Coinbaseea55b8f68f7fbf…062e3912e3e4bc

1 in → 1 out7.3600 XPM110 B

AGtjVNkz…Z6kHj1Lb

b16f2401b01730…90be4bfb64c064

3 in → 2 out21.9800 XPM421 B

AZrinwUb…sQussKcD AT1CT4Cj…94SvacAM

e88cd6e1cb8a09…2a9f8a81324781

1 in → 2 out7.3100 XPM193 B

AZ64kfaM…okEVdQKN AVEfhJ1b…G1HPVjLz

b79d9eed9b0dd6…8d034ba7261d24

2 in → 2 out6.5744 XPM374 B

AKmW9Tje…kCLwCrwy ATEumkjo…vFCRtHwP

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.

2.083 × 10⁹⁵(96-digit number)

20831287801119750293…12747211185091142399

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

2.083 × 10⁹⁵(96-digit number)

20831287801119750293…12747211185091142399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.083 × 10⁹⁵(96-digit number)

20831287801119750293…12747211185091142401

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

4.166 × 10⁹⁵(96-digit number)

41662575602239500586…25494422370182284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.166 × 10⁹⁵(96-digit number)

41662575602239500586…25494422370182284801

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

8.332 × 10⁹⁵(96-digit number)

83325151204479001173…50988844740364569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.332 × 10⁹⁵(96-digit number)

83325151204479001173…50988844740364569601

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

1.666 × 10⁹⁶(97-digit number)

16665030240895800234…01977689480729139199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.666 × 10⁹⁶(97-digit number)

16665030240895800234…01977689480729139201

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

3.333 × 10⁹⁶(97-digit number)

33330060481791600469…03955378961458278399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.333 × 10⁹⁶(97-digit number)

33330060481791600469…03955378961458278401

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

6.666 × 10⁹⁶(97-digit number)

66660120963583200938…07910757922916556799

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 #2,862,736

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