Block #360,088

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/15/2014, 5:37:30 AM · Difficulty 10.3899 · 6,431,876 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

99919e2aa59341ad8285101ccd6db2d6e9a84f33e514aad55492fcef8eb5c749

View on Chainz ↗

Height

#360,088

Difficulty

10.389856

Transactions

Size

2.38 KB

Version

Bits

0a63cd93

Nonce

106,426

Timestamp

1/15/2014, 5:37:30 AM

Confirmations

6,431,876

Merkle Root

a91d434ec6962fa2d4ae5513ebfeccd4ae25c9ddc43bfb02662d7c6a1ea9e0b4

Transactions (4)

Coinbase75f473bc95dcd9…9732290f238899

1 in → 21 out9.2500 XPM777 B

AQvZBsUo…hppgRZTJ Aac9Hjdg…P4ktypc3 AZV4TwxQ…8JnQqSoH AWCVEa7p…3vPBmiA2 ATKK7iFz…wZm46KN1

03c233ff9e2432…cb24e6d7450b7a

2 in → 2 out12.6041 XPM373 B

ATZUp49D…xaoNMsmK ARkptCC5…KZQ9mVdi

005c3425c97c2e…cb5fa452e32181

6 in → 2 out15.0160 XPM966 B

AezKQSS9…UH3WeAj9 AHJZe99R…VN5agbar

23954cda03cb88…e27f6d87d92319

1 in → 2 out7.2081 XPM226 B

AM8Yq3Te…LyhBPrB3 AGusNSbi…TMhj3ShN

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.

6.394 × 10⁹⁴(95-digit number)

63940835098849527183…83296034508486270199

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

6.394 × 10⁹⁴(95-digit number)

63940835098849527183…83296034508486270199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.394 × 10⁹⁴(95-digit number)

63940835098849527183…83296034508486270201

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

1.278 × 10⁹⁵(96-digit number)

12788167019769905436…66592069016972540399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.278 × 10⁹⁵(96-digit number)

12788167019769905436…66592069016972540401

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

2.557 × 10⁹⁵(96-digit number)

25576334039539810873…33184138033945080799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.557 × 10⁹⁵(96-digit number)

25576334039539810873…33184138033945080801

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

5.115 × 10⁹⁵(96-digit number)

51152668079079621747…66368276067890161599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.115 × 10⁹⁵(96-digit number)

51152668079079621747…66368276067890161601

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

1.023 × 10⁹⁶(97-digit number)

10230533615815924349…32736552135780323199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.023 × 10⁹⁶(97-digit number)

10230533615815924349…32736552135780323201

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