Block #1,753,729

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/8/2016, 6:47:53 PM · Difficulty 10.6996 · 5,054,160 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

190b50a49f34b725569150aac1c0e7644d6f07ecff0c9a1609d05a508c557656

View on Chainz ↗

Height

#1,753,729

Difficulty

10.699552

Transactions

Size

5.74 KB

Version

Bits

0ab315d6

Nonce

317,251,012

Timestamp

9/8/2016, 6:47:53 PM

Confirmations

5,054,160

Mined by

⛏️ P2SHAegKQGSjgdpRs2fuqzT71zR9SYaw5ZXdCr

Merkle Root

f3be0a80b1c679143d2413acb199293a31e4639008c870d903c2db127e2ff805

Transactions (4)

Coinbase54b3fcd99f2e42…296f616e850a27

1 in → 1 out8.7800 XPM109 B

AegKQGSj…aw5ZXdCr

0dfe3b7a6a2ea3…5aca445cc16104

1 in → 51 out129.8114 XPM1.85 KB

AFwguNUY…Eob2YrGp AWJrh5Mu…hYqPAfL6 AXsSKTsT…JUXzZiKb ARKN9NJk…zEKciLXS AJMSd7rM…vRiHWBzu

e0aef3f44ef47f…157275319a482a

1 in → 51 out59.6208 XPM1.85 KB

AGbkEmh6…jGAK9g9R AVA234pf…hfXcvGVm AVwD1kG2…tyMfzCA5 AQfuoVnd…M87kb7Xo AYoCgkjV…xcHhUu3q

133171d8c65731…939f7996b6ccaf

1 in → 51 out4.9790 XPM1.85 KB

AMt426QN…6t8TfxPj AMm7B5tm…vNu8By9B AUc7wQRN…ZHSKvzM8 AZgvzcHz…xUqoMVic AdRQa5Mq…kj7ew5UF

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.

1.397 × 10⁹³(94-digit number)

13974542738352020354…19563846792314970239

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

1.397 × 10⁹³(94-digit number)

13974542738352020354…19563846792314970239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.397 × 10⁹³(94-digit number)

13974542738352020354…19563846792314970241

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

2.794 × 10⁹³(94-digit number)

27949085476704040708…39127693584629940479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.794 × 10⁹³(94-digit number)

27949085476704040708…39127693584629940481

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

5.589 × 10⁹³(94-digit number)

55898170953408081416…78255387169259880959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.589 × 10⁹³(94-digit number)

55898170953408081416…78255387169259880961

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

1.117 × 10⁹⁴(95-digit number)

11179634190681616283…56510774338519761919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.117 × 10⁹⁴(95-digit number)

11179634190681616283…56510774338519761921

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

2.235 × 10⁹⁴(95-digit number)

22359268381363232566…13021548677039523839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.235 × 10⁹⁴(95-digit number)

22359268381363232566…13021548677039523841

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 #1,753,729

Cookie Preferences