Block #2,137,273

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/29/2017, 9:41:37 PM · Difficulty 10.8892 · 4,707,424 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

cba4a866af81f0ce6f98fb4e94aef87e0cb0f704cf6ec8ad40bf9f5ddc2c16b0

View on Chainz ↗

Height

#2,137,273

Difficulty

10.889239

Transactions

Size

874 B

Version

Bits

0ae3a52b

Nonce

1,789,279,982

Timestamp

5/29/2017, 9:41:37 PM

Confirmations

4,707,424

Mined by

⛏️ P2SHAXTzngvcZVJZw3mDnBqnfdeRBxHP2uoVKp

Merkle Root

5cd4c1ded01c509c6c870e86fa09be69430da00bab9309de907be373cb06e60b

Transactions (4)

Coinbase4b9d20d8764c8b…1b30660f203003

1 in → 1 out8.4500 XPM109 B

AXTzngvc…HP2uoVKp

692a25ee3f75d5…c0ad0ed93ebd83

1 in → 2 out68.5497 XPM225 B

AJCaBMWS…RPhdkyVR AYuK1g5e…gkTPwDbz

bf6e4c2429a130…8ca5fb1119b120

1 in → 2 out58.6397 XPM225 B

Abpcoxrm…uee38vyp AYuK1g5e…gkTPwDbz

30e18db222dd9a…e0285ef8bccd5b

1 in → 2 out48.7297 XPM225 B

AYuK1g5e…gkTPwDbz Aa6pq415…19jNNYYj

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.

1.680 × 10⁹⁵(96-digit number)

16805865669874979450…72989991009317731999

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

1.680 × 10⁹⁵(96-digit number)

16805865669874979450…72989991009317731999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.680 × 10⁹⁵(96-digit number)

16805865669874979450…72989991009317732001

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

3.361 × 10⁹⁵(96-digit number)

33611731339749958900…45979982018635463999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.361 × 10⁹⁵(96-digit number)

33611731339749958900…45979982018635464001

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

6.722 × 10⁹⁵(96-digit number)

67223462679499917800…91959964037270927999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.722 × 10⁹⁵(96-digit number)

67223462679499917800…91959964037270928001

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

1.344 × 10⁹⁶(97-digit number)

13444692535899983560…83919928074541855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.344 × 10⁹⁶(97-digit number)

13444692535899983560…83919928074541856001

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

2.688 × 10⁹⁶(97-digit number)

26889385071799967120…67839856149083711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.688 × 10⁹⁶(97-digit number)

26889385071799967120…67839856149083712001

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 #2,137,273

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