Block #2,681,046

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/28/2018, 3:44:25 AM · Difficulty 11.6916 · 4,125,803 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a5a65c9e89d8180b14993cdb086a33475ee5ef0379b66c7d9b3772dc1ec8315c

View on Chainz ↗

Height

#2,681,046

Difficulty

11.691575

Transactions

Size

1.14 KB

Version

Bits

0bb10b16

Nonce

156,932,351

Timestamp

5/28/2018, 3:44:25 AM

Confirmations

4,125,803

Mined by

⛏️ P2SHAH7umcPkms6YA6e957Kf4CjYigprXxxQYv

Merkle Root

11c3dddfd65bf378b305f7254eb3e64cc82f0a223af551b1495d4331b1c1d9f9

Transactions (2)

Coinbase892594f393b05a…1db226d380f405

1 in → 1 out7.3100 XPM110 B

AH7umcPk…prXxxQYv

0a2f14f4cc23f3…5203d4e7d1ee63

6 in → 2 out11250.0100 XPM966 B

AaLjLh4D…cTQwEGVg AY1sDSVW…AXQK9K95

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.

1.601 × 10⁹⁸(99-digit number)

16018969679232402782…39770337328149954559

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

1.601 × 10⁹⁸(99-digit number)

16018969679232402782…39770337328149954559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.601 × 10⁹⁸(99-digit number)

16018969679232402782…39770337328149954561

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

3.203 × 10⁹⁸(99-digit number)

32037939358464805564…79540674656299909119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.203 × 10⁹⁸(99-digit number)

32037939358464805564…79540674656299909121

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

6.407 × 10⁹⁸(99-digit number)

64075878716929611128…59081349312599818239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.407 × 10⁹⁸(99-digit number)

64075878716929611128…59081349312599818241

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

1.281 × 10⁹⁹(100-digit number)

12815175743385922225…18162698625199636479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.281 × 10⁹⁹(100-digit number)

12815175743385922225…18162698625199636481

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

2.563 × 10⁹⁹(100-digit number)

25630351486771844451…36325397250399272959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.563 × 10⁹⁹(100-digit number)

25630351486771844451…36325397250399272961

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

5.126 × 10⁹⁹(100-digit number)

51260702973543688902…72650794500798545919

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 #2,681,046

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