Block #360,084

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 5:39:51 AM · Difficulty 10.3895 · 6,443,583 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f7e935e2df6ac1b8fdf1aa758b9aafdca52adb6d81f5b11349605f1a1759bc86

View on Chainz ↗

Height

#360,084

Difficulty

10.389538

Transactions

Size

1.49 KB

Version

Bits

0a63b8c5

Nonce

114,981

Timestamp

1/15/2014, 5:39:51 AM

Confirmations

6,443,583

Mined by

⛏️ ~uAMQC4aya4xubziAP8jJGG5nLpZc4ptxi3K

Merkle Root

2af6b2d66ef0aab04864caae99a88692f6fee762c017ee31b4d5b71ef075e5af

Transactions (5)

Coinbasee1173bd530d51b…f91836394bd488

1 in → 5 out9.2900 XPM233 B

AMQC4aya…c4ptxi3K AKMBvL7P…npwgm5sY AakJsGaf…CSFKrp9K ARpndEmc…Hg792kEk AJno7LX2…vo4wdWtY

20ea3339fc8851…b49354b828ed29

3 in → 2 out79.0516 XPM523 B

ASF31wYi…42B7qC7u Acg2x6Pz…Nw9uFzDA

2092a8e9c12ae2…9219ebc6657049

1 in → 2 out6.1451 XPM225 B

ALTCG2Cr…WBCjawP2 AMycoGpr…hm6j3cMW

86a1e4580b9995…6ab80d6297bc92

1 in → 2 out4.1934 XPM226 B

AXxp24rY…yi3yUFBu AJPqbTCH…yKSHSwzP

53da8f401653a1…b06450ae47a64d

1 in → 2 out3.1943 XPM226 B

ANcdoBAC…1asQq487 ANoc8GRr…L6WooGzJ

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.

8.501 × 10⁹¹(92-digit number)

85016349765855298990…25631946165894420479

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

8.501 × 10⁹¹(92-digit number)

85016349765855298990…25631946165894420479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.501 × 10⁹¹(92-digit number)

85016349765855298990…25631946165894420481

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

1.700 × 10⁹²(93-digit number)

17003269953171059798…51263892331788840959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.700 × 10⁹²(93-digit number)

17003269953171059798…51263892331788840961

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

3.400 × 10⁹²(93-digit number)

34006539906342119596…02527784663577681919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.400 × 10⁹²(93-digit number)

34006539906342119596…02527784663577681921

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

6.801 × 10⁹²(93-digit number)

68013079812684239192…05055569327155363839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.801 × 10⁹²(93-digit number)

68013079812684239192…05055569327155363841

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

1.360 × 10⁹³(94-digit number)

13602615962536847838…10111138654310727679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.360 × 10⁹³(94-digit number)

13602615962536847838…10111138654310727681

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