Block #2,666,059

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/18/2018, 12:48:33 AM · Difficulty 11.6647 · 4,166,472 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e6d1befc982b4dd6a8344215e48186a0d6e15aa214b7b8fff5120c73c99485a0

View on Chainz ↗

Height

#2,666,059

Difficulty

11.664662

Transactions

Size

800 B

Version

Bits

0baa2745

Nonce

1,285,085,626

Timestamp

5/18/2018, 12:48:33 AM

Confirmations

4,166,472

Mined by

⛏️ P2SHALGwXSMGfer4tb3Thmku1QQz5gdYVbFK7o

Merkle Root

1c1c2c63d9ba63a7d6fd49d5f6b2794aa557203505c3375836a1189019e96f3a

Transactions (3)

Coinbase5828f6997f98f8…829aaf44729b49

1 in → 1 out7.3600 XPM110 B

ALGwXSMG…dYVbFK7o

ac7439ba097456…6fbdc9ddf7eefb

1 in → 2 out6.2270 XPM226 B

AMpp4Ae3…dvQUfdbU AdQESrxq…r5NhoR53

d237f3b76ca341…0b092653c8b6ba

2 in → 2 out5.8557 XPM374 B

AW4vm7K2…CyKApbJi ARXFP2VU…fTWeozav

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.

1.661 × 10⁹⁵(96-digit number)

16618321761672611228…28637243149155778559

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

1.661 × 10⁹⁵(96-digit number)

16618321761672611228…28637243149155778559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.661 × 10⁹⁵(96-digit number)

16618321761672611228…28637243149155778561

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

3.323 × 10⁹⁵(96-digit number)

33236643523345222456…57274486298311557119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.323 × 10⁹⁵(96-digit number)

33236643523345222456…57274486298311557121

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

6.647 × 10⁹⁵(96-digit number)

66473287046690444912…14548972596623114239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.647 × 10⁹⁵(96-digit number)

66473287046690444912…14548972596623114241

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

1.329 × 10⁹⁶(97-digit number)

13294657409338088982…29097945193246228479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.329 × 10⁹⁶(97-digit number)

13294657409338088982…29097945193246228481

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

2.658 × 10⁹⁶(97-digit number)

26589314818676177964…58195890386492456959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.658 × 10⁹⁶(97-digit number)

26589314818676177964…58195890386492456961

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

5.317 × 10⁹⁶(97-digit number)

53178629637352355929…16391780772984913919

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 #2,666,059

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