Block #3,102,862

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/21/2019, 2:51:39 AM · Difficulty 11.1693 · 3,738,722 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a87b9bce8d81cda041465e6fa5ab5e0d1cc31bc7712d2e3bf21f9233faccf410

View on Chainz ↗

Height

#3,102,862

Difficulty

11.169278

Transactions

Size

1.47 KB

Version

Bits

0b2b55ca

Nonce

1,510,714,575

Timestamp

3/21/2019, 2:51:39 AM

Confirmations

3,738,722

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

0c71b30f525bd5d451c194b56831dd6b95e7b910d50372e1070cbe0db9c009e3

Transactions (3)

Coinbasec6e60af540cf28…88a2a7c8aa2f15

1 in → 1 out8.0500 XPM110 B

AbXwmGxD…4XXYP765

4e9a4ac8e2ccd7…0a9d1d5f9de2ab

7 in → 2 out3548.7700 XPM1.09 KB

AKs7KtPK…HxhFHyKF AeqykYSj…zod9fT1j

0ab979f52359f6…7e7264dc533705

1 in → 2 out8.0700 XPM193 B

AJtQNmM4…XBRjaQ6m AbXwmGxD…4XXYP765

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.

2.312 × 10⁹⁶(97-digit number)

23124646972909593089…50127075529837491199

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

2.312 × 10⁹⁶(97-digit number)

23124646972909593089…50127075529837491199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.312 × 10⁹⁶(97-digit number)

23124646972909593089…50127075529837491201

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

4.624 × 10⁹⁶(97-digit number)

46249293945819186179…00254151059674982399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.624 × 10⁹⁶(97-digit number)

46249293945819186179…00254151059674982401

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

9.249 × 10⁹⁶(97-digit number)

92498587891638372358…00508302119349964799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

9.249 × 10⁹⁶(97-digit number)

92498587891638372358…00508302119349964801

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

1.849 × 10⁹⁷(98-digit number)

18499717578327674471…01016604238699929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.849 × 10⁹⁷(98-digit number)

18499717578327674471…01016604238699929601

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

3.699 × 10⁹⁷(98-digit number)

36999435156655348943…02033208477399859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.699 × 10⁹⁷(98-digit number)

36999435156655348943…02033208477399859201

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

7.399 × 10⁹⁷(98-digit number)

73998870313310697886…04066416954799718399

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 #3,102,862

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