Block #928,700

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/9/2015, 7:07:15 AM · Difficulty 10.9037 · 5,880,954 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13c061aac666d1653a9430bbe4208cc75b729df6f7722e6eb36b0d16d9eb3b73

View on Chainz ↗

Height

#928,700

Difficulty

10.903676

Transactions

Size

3.08 KB

Version

Bits

0ae75757

Nonce

1,332,912,933

Timestamp

2/9/2015, 7:07:15 AM

Confirmations

5,880,954

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3ca8351f800289bd0c5c06cb7e1f0d5f89448b980870b2c9ecfa93c2ccf93dde

Transactions (4)

Coinbase560ee8ca438344…02c00e541f9295

1 in → 1 out8.4500 XPM116 B

ANSXnLY2…Sd25TjkD

92b4c29ad014ba…07f0baafce44c0

2 in → 1 out16.8800 XPM274 B

AL28HEd6…UEWKLHFr

e22224a107fd51…6b0889d1896cc0

13 in → 2 out105.7736 XPM1.95 KB

AH1Porpk…pjuNCGNm AZVYgfkV…TMEW8Yij

149ef37d86461d…49ac7b67964b83

4 in → 2 out23.3902 XPM671 B

AdhxuKrc…YaxSCm4p AMGsG8ma…txBDFaAi

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.

2.116 × 10⁹⁸(99-digit number)

21161805953739330005…28590446843947315199

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

2.116 × 10⁹⁸(99-digit number)

21161805953739330005…28590446843947315199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.116 × 10⁹⁸(99-digit number)

21161805953739330005…28590446843947315201

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

4.232 × 10⁹⁸(99-digit number)

42323611907478660010…57180893687894630399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.232 × 10⁹⁸(99-digit number)

42323611907478660010…57180893687894630401

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

8.464 × 10⁹⁸(99-digit number)

84647223814957320020…14361787375789260799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.464 × 10⁹⁸(99-digit number)

84647223814957320020…14361787375789260801

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

1.692 × 10⁹⁹(100-digit number)

16929444762991464004…28723574751578521599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.692 × 10⁹⁹(100-digit number)

16929444762991464004…28723574751578521601

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

3.385 × 10⁹⁹(100-digit number)

33858889525982928008…57447149503157043199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.385 × 10⁹⁹(100-digit number)

33858889525982928008…57447149503157043201

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 #928,700

Cookie Preferences