Block #2,087,650

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/25/2017, 7:43:52 PM · Difficulty 10.8747 · 4,744,921 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

542f074fd8569cbb99e89b1de8b3a0e8ec65ebfca6cdea990d2300f54a23009e

View on Chainz ↗

Height

#2,087,650

Difficulty

10.874700

Transactions

Size

1.68 KB

Version

Bits

0adfec5e

Nonce

1,860,179,606

Timestamp

4/25/2017, 7:43:52 PM

Confirmations

4,744,921

Mined by

⛏️ P2SHAbZzboavhcCAyVq6rK13BqBaM8PEKBPjov

Merkle Root

f214fe7f5ae2d4b55f69f27016173a2f5b079ffea83e19a3386ad97783c02e8e

Transactions (2)

Coinbase487a533bb34e1a…fa6fe4eee20612

1 in → 1 out8.4600 XPM109 B

AbZzboav…PEKBPjov

c658ac0fd616e7…bb6553610bbd56

10 in → 1 out546.5728 XPM1.49 KB

AYoy228q…feZqXfNq

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.

4.606 × 10⁹⁶(97-digit number)

46061167874571501346…65070308938481080319

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

4.606 × 10⁹⁶(97-digit number)

46061167874571501346…65070308938481080319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.606 × 10⁹⁶(97-digit number)

46061167874571501346…65070308938481080321

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

9.212 × 10⁹⁶(97-digit number)

92122335749143002692…30140617876962160639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.212 × 10⁹⁶(97-digit number)

92122335749143002692…30140617876962160641

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

1.842 × 10⁹⁷(98-digit number)

18424467149828600538…60281235753924321279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.842 × 10⁹⁷(98-digit number)

18424467149828600538…60281235753924321281

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

3.684 × 10⁹⁷(98-digit number)

36848934299657201076…20562471507848642559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.684 × 10⁹⁷(98-digit number)

36848934299657201076…20562471507848642561

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

7.369 × 10⁹⁷(98-digit number)

73697868599314402153…41124943015697285119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.369 × 10⁹⁷(98-digit number)

73697868599314402153…41124943015697285121

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

1.473 × 10⁹⁸(99-digit number)

14739573719862880430…82249886031394570239

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 #2,087,650

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