Block #922,306

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 2/4/2015, 9:09:07 AM · Difficulty 10.9157 · 5,882,967 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

75b15bd08bb22ccd766894acfd0abe3dfe7e8c2427c2406a25626573c0d01754

View on Chainz ↗

Height

#922,306

Difficulty

10.915744

Transactions

Size

115.96 KB

Version

Bits

0aea6e32

Nonce

1,941,344,317

Timestamp

2/4/2015, 9:09:07 AM

Confirmations

5,882,967

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b5209bba003647fa62b0a2659aa8cac5961bd729447052614e7b528b6852c570

Transactions (5)

Coinbase9b2bcf646ce187…025ccb98d8c7a8

1 in → 1 out9.5800 XPM116 B

ANSXnLY2…Sd25TjkD

0efac5489d42a8…8f06a40eb65156

200 in → 1 out1103.3631 XPM28.96 KB

AKuP4XsJ…owbodNxQ

935e4d1ae1d71e…c43f9a4827f53c

200 in → 1 out936.5627 XPM28.93 KB

AKuP4XsJ…owbodNxQ

41076cccd0756c…302b4c648e425c

200 in → 1 out1016.9775 XPM28.93 KB

AKuP4XsJ…owbodNxQ

b1c7744db6405d…99c4b752b35bb5

200 in → 1 out939.5874 XPM28.93 KB

AKuP4XsJ…owbodNxQ

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.

1.000 × 10⁹⁶(97-digit number)

10006337011242947979…76777471518816273919

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

1.000 × 10⁹⁶(97-digit number)

10006337011242947979…76777471518816273919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.000 × 10⁹⁶(97-digit number)

10006337011242947979…76777471518816273921

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

2.001 × 10⁹⁶(97-digit number)

20012674022485895958…53554943037632547839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.001 × 10⁹⁶(97-digit number)

20012674022485895958…53554943037632547841

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

4.002 × 10⁹⁶(97-digit number)

40025348044971791916…07109886075265095679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.002 × 10⁹⁶(97-digit number)

40025348044971791916…07109886075265095681

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

8.005 × 10⁹⁶(97-digit number)

80050696089943583832…14219772150530191359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.005 × 10⁹⁶(97-digit number)

80050696089943583832…14219772150530191361

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

1.601 × 10⁹⁷(98-digit number)

16010139217988716766…28439544301060382719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.601 × 10⁹⁷(98-digit number)

16010139217988716766…28439544301060382721

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

3.202 × 10⁹⁷(98-digit number)

32020278435977433533…56879088602120765439

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