Block #2,722,099

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/26/2018, 11:34:33 AM · Difficulty 11.6118 · 4,121,325 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

eb4789c0a7bdb4778c56f9dfea5b1df1c26548b0ed98021125deeff76ad658fb

View on Chainz ↗

Height

#2,722,099

Difficulty

11.611776

Transactions

Size

1.42 KB

Version

Bits

0b9c9d5d

Nonce

779,509,068

Timestamp

6/26/2018, 11:34:33 AM

Confirmations

4,121,325

Mined by

⛏️ P2SHAe5smbAagmwV6ziEmSSUrtuFR5iqSqC1Vj

Merkle Root

26a9721217b12d376936d27d9161ca3030a1c11d053820243d9e16dcd64ca1da

Transactions (5)

Coinbase32aca48903c1f5…201e498b49ddb5

1 in → 1 out7.4400 XPM110 B

Ae5smbAa…iqSqC1Vj

9019c8059650a2…1c8a603a9e0aee

1 in → 2 out7.3900 XPM192 B

AaHLF8TJ…vqFM7x91 AbVRRazK…SnoMkLKU

c528767313809c…8d20601c6fe5c5

1 in → 2 out7.3900 XPM192 B

ANCRJ4YX…SuqgdoRe AbYjSPua…VmQLkCLP

cc183b51b51987…b268e671f6f11c

2 in → 2 out8.1200 XPM342 B

AdGFnV3a…o6n2zX3x AVjTh8uw…u1LMwpiH

12dcb49762ed68…e35bc1d88ed3e2

3 in → 2 out4.1600 XPM522 B

Ae73fR6A…zEGMGTg3 AcjyqRFB…JMwMkg4u

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.

1.717 × 10⁹⁶(97-digit number)

17176784040884964927…81687195497331527679

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

1.717 × 10⁹⁶(97-digit number)

17176784040884964927…81687195497331527679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.717 × 10⁹⁶(97-digit number)

17176784040884964927…81687195497331527681

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

3.435 × 10⁹⁶(97-digit number)

34353568081769929855…63374390994663055359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.435 × 10⁹⁶(97-digit number)

34353568081769929855…63374390994663055361

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

6.870 × 10⁹⁶(97-digit number)

68707136163539859710…26748781989326110719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.870 × 10⁹⁶(97-digit number)

68707136163539859710…26748781989326110721

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

1.374 × 10⁹⁷(98-digit number)

13741427232707971942…53497563978652221439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.374 × 10⁹⁷(98-digit number)

13741427232707971942…53497563978652221441

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

2.748 × 10⁹⁷(98-digit number)

27482854465415943884…06995127957304442879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.748 × 10⁹⁷(98-digit number)

27482854465415943884…06995127957304442881

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

5.496 × 10⁹⁷(98-digit number)

54965708930831887768…13990255914608885759

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 #2,722,099

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