Block #289,271

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/2/2013, 3:18:10 AM · Difficulty 9.9884 · 6,510,179 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c70ace79fdc67e74f31c627ecbf994f352163a485706a8a4bc2a9788449ec94

View on Chainz ↗

Height

#289,271

Difficulty

9.988390

Transactions

Size

1.23 KB

Version

Bits

09fd071e

Nonce

18,581

Timestamp

12/2/2013, 3:18:10 AM

Confirmations

6,510,179

Mined by

⛏️ iaRAKEwr54iEsuosjdBu66r2F564f9BfmMkRh

Merkle Root

5c2c4d43a8d47d55ef2ee950f00c12cd43dbb6ca3e736bca8467d096c87f4985

Transactions (2)

Coinbasec3fa49186703aa…bf3d279e43d1b3

1 in → 27 out10.0100 XPM981 B

AKEwr54i…9BfmMkRh AYcLTeXR…bscgPops Ae58nAEb…GFUA15fv AZ2pPuKg…95SN2Yr7 AN63YyQR…1tfe566A

e0bb92d57a657f…98eff8cd052248

1 in → 1 out3.0021 XPM191 B

Aa4j7Xid…6yzja4gg

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.

1.749 × 10⁹³(94-digit number)

17490032918489000238…74814145235677579199

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

1.749 × 10⁹³(94-digit number)

17490032918489000238…74814145235677579199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.749 × 10⁹³(94-digit number)

17490032918489000238…74814145235677579201

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

3.498 × 10⁹³(94-digit number)

34980065836978000477…49628290471355158399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.498 × 10⁹³(94-digit number)

34980065836978000477…49628290471355158401

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

6.996 × 10⁹³(94-digit number)

69960131673956000955…99256580942710316799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.996 × 10⁹³(94-digit number)

69960131673956000955…99256580942710316801

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

1.399 × 10⁹⁴(95-digit number)

13992026334791200191…98513161885420633599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.399 × 10⁹⁴(95-digit number)

13992026334791200191…98513161885420633601

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

2.798 × 10⁹⁴(95-digit number)

27984052669582400382…97026323770841267199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.798 × 10⁹⁴(95-digit number)

27984052669582400382…97026323770841267201

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