Block #2,676,195

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/24/2018, 4:50:46 PM · Difficulty 11.6988 · 4,162,033 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a92d95dcf1fc7608c191a357d1ea5c9d0e5a9981337c2df2d19f7961589cf27d

View on Chainz ↗

Height

#2,676,195

Difficulty

11.698839

Transactions

Size

873 B

Version

Bits

0bb2e721

Nonce

305,879,588

Timestamp

5/24/2018, 4:50:46 PM

Confirmations

4,162,033

Mined by

⛏️ P2SHAZmnwMpvPpPRQ4N4Vc8WzeeHKp2oVRuA4P

Merkle Root

7f84ad33bd397a0265540edff20ccfd384ce1e4b9c569ad368a7c5c99412e086

Transactions (2)

Coinbase089d116a69e2c9…934cc52b7c768b

1 in → 1 out7.3100 XPM110 B

AZmnwMpv…2oVRuA4P

f0bdc971a4d1dc…6ee09128c2cca8

4 in → 2 out4000.0099 XPM672 B

AH3A2GJU…NLYdkucb AG9SNHXB…pX14fg8r

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.

9.604 × 10⁹⁶(97-digit number)

96043713920146915139…08180017018646681599

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

9.604 × 10⁹⁶(97-digit number)

96043713920146915139…08180017018646681599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.604 × 10⁹⁶(97-digit number)

96043713920146915139…08180017018646681601

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

1.920 × 10⁹⁷(98-digit number)

19208742784029383027…16360034037293363199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.920 × 10⁹⁷(98-digit number)

19208742784029383027…16360034037293363201

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

3.841 × 10⁹⁷(98-digit number)

38417485568058766055…32720068074586726399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.841 × 10⁹⁷(98-digit number)

38417485568058766055…32720068074586726401

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

7.683 × 10⁹⁷(98-digit number)

76834971136117532111…65440136149173452799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.683 × 10⁹⁷(98-digit number)

76834971136117532111…65440136149173452801

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

1.536 × 10⁹⁸(99-digit number)

15366994227223506422…30880272298346905599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.536 × 10⁹⁸(99-digit number)

15366994227223506422…30880272298346905601

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

3.073 × 10⁹⁸(99-digit number)

30733988454447012844…61760544596693811199

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 #2,676,195

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