Block #714,244

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 9/9/2014, 9:43:27 PM · Difficulty 10.9554 · 6,092,943 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

52f7405e8c691ff62f767649c002ba611aca633fbcc1ea0ab0d6df07c6f55659

View on Chainz ↗

Height

#714,244

Difficulty

10.955364

Transactions

Size

7.95 KB

Version

Bits

0af492bb

Nonce

731,888,145

Timestamp

9/9/2014, 9:43:27 PM

Confirmations

6,092,943

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4630dfb5e16e538552a3ec1c4901689fd33f0d057bc97c8f5f787fb6d46ec9b5

Transactions (2)

Coinbase1c3e7663cb2b48…14f25520c5ec87

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

038d60597ca42a…915485dd32f670

53 in → 2 out788.4258 XPM7.75 KB

AZUvYfpX…eimiqxQo AZP2roFC…bwVPYDcv

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.

3.098 × 10⁹⁵(96-digit number)

30984715168097079078…45315519353482803199

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

3.098 × 10⁹⁵(96-digit number)

30984715168097079078…45315519353482803199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.098 × 10⁹⁵(96-digit number)

30984715168097079078…45315519353482803201

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

6.196 × 10⁹⁵(96-digit number)

61969430336194158157…90631038706965606399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.196 × 10⁹⁵(96-digit number)

61969430336194158157…90631038706965606401

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

1.239 × 10⁹⁶(97-digit number)

12393886067238831631…81262077413931212799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.239 × 10⁹⁶(97-digit number)

12393886067238831631…81262077413931212801

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

2.478 × 10⁹⁶(97-digit number)

24787772134477663263…62524154827862425599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.478 × 10⁹⁶(97-digit number)

24787772134477663263…62524154827862425601

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

4.957 × 10⁹⁶(97-digit number)

49575544268955326526…25048309655724851199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.957 × 10⁹⁶(97-digit number)

49575544268955326526…25048309655724851201

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

9.915 × 10⁹⁶(97-digit number)

99151088537910653052…50096619311449702399

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 #714,244

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