Block #727,634

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/18/2014, 2:56:48 PM · Difficulty 10.9625 · 6,078,426 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d790fded4dfdb781353e1aa647c153043e99e05dd13b48de8b162ff749aeff7

View on Chainz ↗

Height

#727,634

Difficulty

10.962537

Transactions

Size

22.20 KB

Version

Bits

0af668cb

Nonce

539,176,431

Timestamp

9/18/2014, 2:56:48 PM

Confirmations

6,078,426

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4128b74f1245c4fa12ad84d5c780dbfcfad8405beaec9975d1f738af63293526

Transactions (5)

Coinbase239aee85b51e3e…8a556805db3f83

1 in → 1 out8.5700 XPM116 B

ANSXnLY2…Sd25TjkD

02c580842a0f0e…29a6bc6d1cd300

147 in → 2 out100.0100 XPM21.33 KB

AdyrKCWo…sSgRVVoJ AUDLj1yW…knQzjcRP

32a8d9ba51a0b3…a99011d1622bd6

1 in → 2 out8.3000 XPM227 B

AcuH1Tg5…otyZeLro AVeoKEHW…hGQjMhDV

fcce080c158ac3…7ef3cc86ca5a93

1 in → 2 out8.3000 XPM225 B

ASTkT7H4…KPmA3ZAZ AUfZq9jz…xEGBvByx

462cb28afda540…7d9f0657a76c31

1 in → 2 out8.3000 XPM227 B

AYLX7a4m…2yUFyoRS AXiN448S…vbShp5d5

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.

8.602 × 10⁹⁷(98-digit number)

86026382365798380265…94706738418077547519

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

8.602 × 10⁹⁷(98-digit number)

86026382365798380265…94706738418077547519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.602 × 10⁹⁷(98-digit number)

86026382365798380265…94706738418077547521

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

1.720 × 10⁹⁸(99-digit number)

17205276473159676053…89413476836155095039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.720 × 10⁹⁸(99-digit number)

17205276473159676053…89413476836155095041

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

3.441 × 10⁹⁸(99-digit number)

34410552946319352106…78826953672310190079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.441 × 10⁹⁸(99-digit number)

34410552946319352106…78826953672310190081

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

6.882 × 10⁹⁸(99-digit number)

68821105892638704212…57653907344620380159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.882 × 10⁹⁸(99-digit number)

68821105892638704212…57653907344620380161

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

1.376 × 10⁹⁹(100-digit number)

13764221178527740842…15307814689240760319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.376 × 10⁹⁹(100-digit number)

13764221178527740842…15307814689240760321

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