Block #368,939

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/21/2014, 1:41:55 AM · Difficulty 10.4447 · 6,457,785 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b363a6a782e0abab5170e068465ffb56b1c0e62647ee1453c954f28e1078e91a

View on Chainz ↗

Height

#368,939

Difficulty

10.444700

Transactions

Size

806 B

Version

Bits

0a71d7e1

Nonce

624,708

Timestamp

1/21/2014, 1:41:55 AM

Confirmations

6,457,785

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6a4855e79ad949ef1447bb185ed23c6d3aedace2f2f48846b87795166d4d6d34

Transactions (3)

Coinbasef0eabef57b4e85…e4d438590ceadb

1 in → 1 out9.1700 XPM116 B

AbwWkWZt…kawDhufa

e3cb695961a387…b30c3eacc987d3

2 in → 2 out5.4293 XPM374 B

AWhqCNs1…mTz9bU71 ANhTTrhu…4SbCX4o9

ce185154c8875f…28175f816f89a5

1 in → 2 out4.1175 XPM226 B

AHvTgFGv…L431Xj1C ALfuXYmj…7CNyokSf

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.

8.532 × 10⁹⁴(95-digit number)

85329234560783541234…59715060425839490079

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

8.532 × 10⁹⁴(95-digit number)

85329234560783541234…59715060425839490079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.532 × 10⁹⁴(95-digit number)

85329234560783541234…59715060425839490081

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

1.706 × 10⁹⁵(96-digit number)

17065846912156708246…19430120851678980159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.706 × 10⁹⁵(96-digit number)

17065846912156708246…19430120851678980161

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

3.413 × 10⁹⁵(96-digit number)

34131693824313416493…38860241703357960319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.413 × 10⁹⁵(96-digit number)

34131693824313416493…38860241703357960321

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

6.826 × 10⁹⁵(96-digit number)

68263387648626832987…77720483406715920639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.826 × 10⁹⁵(96-digit number)

68263387648626832987…77720483406715920641

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

1.365 × 10⁹⁶(97-digit number)

13652677529725366597…55440966813431841279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.365 × 10⁹⁶(97-digit number)

13652677529725366597…55440966813431841281

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 #368,939

Cookie Preferences