Block #892,288

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/12/2015, 11:54:40 AM · Difficulty 10.9522 · 5,918,842 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

74ee9f45fe32150a237a771ffcf0cb6f96661a15c15ece9d5fdc94fc436e53fe

View on Chainz ↗

Height

#892,288

Difficulty

10.952216

Transactions

Size

955 B

Version

Bits

0af3c475

Nonce

940,825,997

Timestamp

1/12/2015, 11:54:40 AM

Confirmations

5,918,842

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4318563e8a2f7ae3e77dbbae52613eb2b6c93322922755fc4b48496867b26c52

Transactions (3)

Coinbase2876794a9977e2…acb89e13199b38

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

1655acad0270ca…35084f6418674b

1 in → 2 out6.9888 XPM226 B

AHRoBSh4…BSVTQ36Q ANS29J1d…ZKRTNAkQ

203d5a3aac5ed3…2773453813cc81

3 in → 2 out0.7745 XPM522 B

ALP6szJY…eEPSo5sX Ab3Cb6p9…L3byQzrg

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.

1.135 × 10⁹⁶(97-digit number)

11357001556740980416…13905182654882277999

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

1.135 × 10⁹⁶(97-digit number)

11357001556740980416…13905182654882277999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.135 × 10⁹⁶(97-digit number)

11357001556740980416…13905182654882278001

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

2.271 × 10⁹⁶(97-digit number)

22714003113481960833…27810365309764555999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.271 × 10⁹⁶(97-digit number)

22714003113481960833…27810365309764556001

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

4.542 × 10⁹⁶(97-digit number)

45428006226963921667…55620730619529111999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.542 × 10⁹⁶(97-digit number)

45428006226963921667…55620730619529112001

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

9.085 × 10⁹⁶(97-digit number)

90856012453927843335…11241461239058223999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.085 × 10⁹⁶(97-digit number)

90856012453927843335…11241461239058224001

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

1.817 × 10⁹⁷(98-digit number)

18171202490785568667…22482922478116447999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.817 × 10⁹⁷(98-digit number)

18171202490785568667…22482922478116448001

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 #892,288

Cookie Preferences