Block #2,157,245

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/12/2017, 5:19:31 AM · Difficulty 10.9059 · 4,684,692 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

371c6c4dc84180a8700da0742c9f0b509eb93e91a49ab00d671e78843bace3bb

View on Chainz ↗

Height

#2,157,245

Difficulty

10.905935

Transactions

Size

866 B

Version

Bits

0ae7eb62

Nonce

1,190,109,178

Timestamp

6/12/2017, 5:19:31 AM

Confirmations

4,684,692

Mined by

⛏️ P2SHAWsphFAWPFuVDxDa6NaiNjftvP8TabSGXR

Merkle Root

728297e22ee858e57ede8f38dd3e28b9eb8af3a6bf63a705049013d018bf0763

Transactions (2)

Coinbasef4e60f5c56789e…a8caf6ee7338a6

1 in → 1 out8.4000 XPM109 B

AWsphFAW…8TabSGXR

2e707f473ef394…a22302fd9bf353

4 in → 2 out989.0200 XPM667 B

AS8Swa5k…emSJQqiE ALkBpYs6…yZLuAbmZ

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.

8.725 × 10⁹⁵(96-digit number)

87259887973281065065…58228369797872172799

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

8.725 × 10⁹⁵(96-digit number)

87259887973281065065…58228369797872172799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.725 × 10⁹⁵(96-digit number)

87259887973281065065…58228369797872172801

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

1.745 × 10⁹⁶(97-digit number)

17451977594656213013…16456739595744345599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.745 × 10⁹⁶(97-digit number)

17451977594656213013…16456739595744345601

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

3.490 × 10⁹⁶(97-digit number)

34903955189312426026…32913479191488691199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.490 × 10⁹⁶(97-digit number)

34903955189312426026…32913479191488691201

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

6.980 × 10⁹⁶(97-digit number)

69807910378624852052…65826958382977382399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.980 × 10⁹⁶(97-digit number)

69807910378624852052…65826958382977382401

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

1.396 × 10⁹⁷(98-digit number)

13961582075724970410…31653916765954764799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.396 × 10⁹⁷(98-digit number)

13961582075724970410…31653916765954764801

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

2.792 × 10⁹⁷(98-digit number)

27923164151449940821…63307833531909529599

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

Block #2,157,245

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