Block #361,235

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 10:36:49 PM · Difficulty 10.4029 · 6,448,480 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ca914fda4d19074406463d336da8e4915d33b19a818ec2dfb683b48e8a8f362b

View on Chainz ↗

Height

#361,235

Difficulty

10.402894

Transactions

Size

1.18 KB

Version

Bits

0a672410

Nonce

58,199

Timestamp

1/15/2014, 10:36:49 PM

Confirmations

6,448,480

Mined by

AZwyMUeEeU9toUcpBMpkmWZRnerxMQeLU7

Merkle Root

386a9ea1dd5ed04cd9040edb677b3f926d66e3be0baf32f3985316d92143e4f4

Transactions (2)

Coinbase6fd2274d4dcdc2…0d816405f61edc

1 in → 2 out9.2400 XPM131 B

AZwyMUeE…rxMQeLU7 AcaoBAGZ…n7zfVgjk

70079e143904e4…b144c4b8e33456

5 in → 10 out28.5005 XPM988 B

AQ5ExxAB…9aJbrk9H AQmqy6e5…fUqJW2T5 AWWNH4jf…RpBRcuGj AboxPLvW…PscdoEgo AJaQENaD…wRN4nbo6

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.

1.315 × 10⁹⁶(97-digit number)

13153769085314825421…82826522589135436799

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

1.315 × 10⁹⁶(97-digit number)

13153769085314825421…82826522589135436799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.315 × 10⁹⁶(97-digit number)

13153769085314825421…82826522589135436801

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

2.630 × 10⁹⁶(97-digit number)

26307538170629650842…65653045178270873599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.630 × 10⁹⁶(97-digit number)

26307538170629650842…65653045178270873601

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

5.261 × 10⁹⁶(97-digit number)

52615076341259301684…31306090356541747199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.261 × 10⁹⁶(97-digit number)

52615076341259301684…31306090356541747201

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

1.052 × 10⁹⁷(98-digit number)

10523015268251860336…62612180713083494399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.052 × 10⁹⁷(98-digit number)

10523015268251860336…62612180713083494401

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

2.104 × 10⁹⁷(98-digit number)

21046030536503720673…25224361426166988799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.104 × 10⁹⁷(98-digit number)

21046030536503720673…25224361426166988801

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 #361,235

Cookie Preferences