Block #2,653,575

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/8/2018, 12:33:52 PM · Difficulty 11.7359 · 4,177,422 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

be59e5ecee49cfacb54a8ad0f3c3b82ec7b20099fd5d5d3a75601a01feccad42

View on Chainz ↗

Height

#2,653,575

Difficulty

11.735865

Transactions

Size

1.36 KB

Version

Bits

0bbc61a7

Nonce

825,995,271

Timestamp

5/8/2018, 12:33:52 PM

Confirmations

4,177,422

Mined by

⛏️ P2SHAWyvzGDe3p1aFzq6pwz8bMzTPYfe8UKFGn

Merkle Root

73d1d2ceb8e0e67483a0c44f49872f4a2e2c3a887d50ed50c8564fbd8b193fdf

Transactions (3)

Coinbaseb6cece27b6000d…eb2189b1fb8d53

1 in → 1 out7.2700 XPM110 B

AWyvzGDe…fe8UKFGn

2bbe9dd8b8b298…ef851f4e5a8933

2 in → 2 out4.1750 XPM374 B

ALFCjDjB…XEfXtzaq AV7R5GDE…AsqWhPEQ

52d31cf8745fc6…aacb563750f713

5 in → 2 out16.7540 XPM818 B

AKDDR6Aj…Ga2eCPNt AKCSvoxS…pqXFEBhu

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.

1.358 × 10⁹⁶(97-digit number)

13582934589718388152…63377536942642954239

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

1.358 × 10⁹⁶(97-digit number)

13582934589718388152…63377536942642954239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.358 × 10⁹⁶(97-digit number)

13582934589718388152…63377536942642954241

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

2.716 × 10⁹⁶(97-digit number)

27165869179436776305…26755073885285908479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.716 × 10⁹⁶(97-digit number)

27165869179436776305…26755073885285908481

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

5.433 × 10⁹⁶(97-digit number)

54331738358873552611…53510147770571816959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.433 × 10⁹⁶(97-digit number)

54331738358873552611…53510147770571816961

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

1.086 × 10⁹⁷(98-digit number)

10866347671774710522…07020295541143633919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.086 × 10⁹⁷(98-digit number)

10866347671774710522…07020295541143633921

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

2.173 × 10⁹⁷(98-digit number)

21732695343549421044…14040591082287267839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.173 × 10⁹⁷(98-digit number)

21732695343549421044…14040591082287267841

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

4.346 × 10⁹⁷(98-digit number)

43465390687098842089…28081182164574535679

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 #2,653,575

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