Block #716,740

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/11/2014, 9:07:09 PM · Difficulty 10.9523 · 6,108,220 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b0b374e94f4d08b416234556097f664cc57dc22c83e3fb5cd95dbcde97910f45

View on Chainz ↗

Height

#716,740

Difficulty

10.952272

Transactions

Size

1.66 KB

Version

Bits

0af3c81a

Nonce

995,926,614

Timestamp

9/11/2014, 9:07:09 PM

Confirmations

6,108,220

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

67a69a9cf43e833e2c766d606a1a7c891b4ed5636b7fb170d2ba7595600a6ce6

Transactions (4)

Coinbasee2bb1b9ca6b729…f26a53e3503df2

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

31c8973ca8146a…9c9d41599d288d

3 in → 2 out24.9400 XPM524 B

AdTdGjUR…Ymdnfcdx AJwLt2hK…sVKQPZtR

fae64e195c80ba…e4f27d155461f8

4 in → 4 out6.7630 XPM738 B

AHrFNmf8…hpqU2WtU AeKNrjNj…1NEq95Ta AJcmFad4…YNAMFS3w AYk6SdQf…UGcYbb4t

e36897ca56a259…b3166d66d28749

1 in → 2 out1.9160 XPM226 B

AYU1Ynxb…6LNs2ZYM ASWDSxcp…booSVDft

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.

5.685 × 10⁹⁶(97-digit number)

56859490849952142010…43638437868802406399

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

5.685 × 10⁹⁶(97-digit number)

56859490849952142010…43638437868802406399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.685 × 10⁹⁶(97-digit number)

56859490849952142010…43638437868802406401

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

1.137 × 10⁹⁷(98-digit number)

11371898169990428402…87276875737604812799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.137 × 10⁹⁷(98-digit number)

11371898169990428402…87276875737604812801

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

2.274 × 10⁹⁷(98-digit number)

22743796339980856804…74553751475209625599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.274 × 10⁹⁷(98-digit number)

22743796339980856804…74553751475209625601

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

4.548 × 10⁹⁷(98-digit number)

45487592679961713608…49107502950419251199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.548 × 10⁹⁷(98-digit number)

45487592679961713608…49107502950419251201

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

9.097 × 10⁹⁷(98-digit number)

90975185359923427216…98215005900838502399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.097 × 10⁹⁷(98-digit number)

90975185359923427216…98215005900838502401

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

1.819 × 10⁹⁸(99-digit number)

18195037071984685443…96430011801677004799

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 #716,740

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