Block #2,910,143

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 11/4/2018, 6:22:58 PM · Difficulty 11.5355 · 3,929,353 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5e354979735241a4c40507a7c096f7d40b32c6b2866a8f9707fd6aee1861190e

View on Chainz ↗

Height

#2,910,143

Difficulty

11.535540

Transactions

Size

16.62 KB

Version

Bits

0b891929

Nonce

1,741,060,618

Timestamp

11/4/2018, 6:22:58 PM

Confirmations

3,929,353

Mined by

⛏️ P2SHAaSWCRXCw7aW7bJNPFzfaR6Ao1saExFSrh

Merkle Root

0967afce387330ce4571e7cea4a1534aeca8af96a6d3b8b9a5f5a766bf759a72

Transactions (2)

Coinbasece6852b93c8003…f203584ece6c29

1 in → 1 out7.6700 XPM110 B

AaSWCRXC…saExFSrh

1e27980775b0e6…4e76b407bf73e4

113 in → 2 out448.2700 XPM16.42 KB

AZSo9Bzj…amBN2AxG AQRn6yfR…z5FsKtdj

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.

6.691 × 10⁹⁶(97-digit number)

66916975658760376418…08258638172767815679

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

6.691 × 10⁹⁶(97-digit number)

66916975658760376418…08258638172767815679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.691 × 10⁹⁶(97-digit number)

66916975658760376418…08258638172767815681

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

1.338 × 10⁹⁷(98-digit number)

13383395131752075283…16517276345535631359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.338 × 10⁹⁷(98-digit number)

13383395131752075283…16517276345535631361

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

2.676 × 10⁹⁷(98-digit number)

26766790263504150567…33034552691071262719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.676 × 10⁹⁷(98-digit number)

26766790263504150567…33034552691071262721

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

5.353 × 10⁹⁷(98-digit number)

53533580527008301135…66069105382142525439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.353 × 10⁹⁷(98-digit number)

53533580527008301135…66069105382142525441

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

1.070 × 10⁹⁸(99-digit number)

10706716105401660227…32138210764285050879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.070 × 10⁹⁸(99-digit number)

10706716105401660227…32138210764285050881

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

2.141 × 10⁹⁸(99-digit number)

21413432210803320454…64276421528570101759

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 #2,910,143

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