Block #730,566

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/20/2014, 12:05:22 AM · Difficulty 10.9690 · 6,078,496 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

24dd027d5695e54970af3c5c00f8cea146275d2aed9b6cdf5a5c040e5f1bd663

View on Chainz ↗

Height

#730,566

Difficulty

10.969017

Transactions

Size

1.73 KB

Version

Bits

0af8117e

Nonce

718,314,797

Timestamp

9/20/2014, 12:05:22 AM

Confirmations

6,078,496

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

570c86e5dad190f54f2e32e37f54aab2e236144785cbb67ea01cb2fdada61b5e

Transactions (4)

Coinbase71858d0f587a9c…71e8c39ed617e2

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

bbd0813a80dac4…6c37ac1eb11871

6 in → 2 out10.1535 XPM966 B

ATNAKXn4…gNAq5i7m AXeYt2Rh…jQonTT1n

74c71bdb498914…60f3edeb8093b2

2 in → 2 out2.3506 XPM374 B

ARJQsNEx…UvYvuSPW AeKNrjNj…1NEq95Ta

9f05194145a02d…ab72163d1de98e

1 in → 2 out6.6078 XPM226 B

AKP1cCop…zFqY1RtW ATUJFkEF…j71DTZhm

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.

1.107 × 10⁹⁹(100-digit number)

11078692985812405685…15124226277610946559

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

1.107 × 10⁹⁹(100-digit number)

11078692985812405685…15124226277610946559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.107 × 10⁹⁹(100-digit number)

11078692985812405685…15124226277610946561

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

2.215 × 10⁹⁹(100-digit number)

22157385971624811370…30248452555221893119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.215 × 10⁹⁹(100-digit number)

22157385971624811370…30248452555221893121

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

4.431 × 10⁹⁹(100-digit number)

44314771943249622741…60496905110443786239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.431 × 10⁹⁹(100-digit number)

44314771943249622741…60496905110443786241

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

8.862 × 10⁹⁹(100-digit number)

88629543886499245482…20993810220887572479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.862 × 10⁹⁹(100-digit number)

88629543886499245482…20993810220887572481

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

1.772 × 10¹⁰⁰(101-digit number)

17725908777299849096…41987620441775144959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.772 × 10¹⁰⁰(101-digit number)

17725908777299849096…41987620441775144961

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 #730,566

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