Block #2,347,891

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/23/2017, 5:58:43 AM · Difficulty 10.8978 · 4,484,672 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d4eb80edac2f48962cfb978027e157bfcd5dc1bec8173565262a703c9cba827

View on Chainz ↗

Height

#2,347,891

Difficulty

10.897760

Transactions

Size

4.46 KB

Version

Bits

0ae5d395

Nonce

283,097,789

Timestamp

10/23/2017, 5:58:43 AM

Confirmations

4,484,672

Mined by

⛏️ P2SHAZC4EgprZ4J1ddnzqxbCEDkxUK5sQLKQVa

Merkle Root

68a777b5c532cacdf12b732549a588c64a242bc491b49095decf0c0dbe7426af

Transactions (2)

Coinbase134ea78c274d82…794241b16d41ed

1 in → 1 out8.4600 XPM110 B

AZC4Egpr…5sQLKQVa

6fc6a893149a4c…4ce879715b4ecd

29 in → 2 out121.5801 XPM4.27 KB

AR3L4JxU…dwhphEJV AaCRcdyL…iPkDwGwi

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.

6.714 × 10⁹³(94-digit number)

67140640438937763167…78619029823470881279

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

6.714 × 10⁹³(94-digit number)

67140640438937763167…78619029823470881279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.714 × 10⁹³(94-digit number)

67140640438937763167…78619029823470881281

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

1.342 × 10⁹⁴(95-digit number)

13428128087787552633…57238059646941762559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.342 × 10⁹⁴(95-digit number)

13428128087787552633…57238059646941762561

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

2.685 × 10⁹⁴(95-digit number)

26856256175575105267…14476119293883525119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.685 × 10⁹⁴(95-digit number)

26856256175575105267…14476119293883525121

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

5.371 × 10⁹⁴(95-digit number)

53712512351150210534…28952238587767050239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.371 × 10⁹⁴(95-digit number)

53712512351150210534…28952238587767050241

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

1.074 × 10⁹⁵(96-digit number)

10742502470230042106…57904477175534100479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.074 × 10⁹⁵(96-digit number)

10742502470230042106…57904477175534100481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,347,891

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