Block #373,339

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 6:05:52 AM · Difficulty 10.4250 · 6,430,720 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

64f18c268e967b04197aea94b111472912601ce96545455ce6fc11115cd00dc9

View on Chainz ↗

Height

#373,339

Difficulty

10.425044

Transactions

Size

879 B

Version

Bits

0a6ccfb3

Nonce

202,377

Timestamp

1/24/2014, 6:05:52 AM

Confirmations

6,430,720

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

cc37b5681ed84977971736ed66544ce7aaa7190934f950e01924ab8117a392f6

Transactions (4)

Coinbase597579e1317d86…1d3854b52da4b7

1 in → 1 out9.2200 XPM110 B

AeKNrjNj…1NEq95Ta

4e3015d9ca4190…ed1135c1e79b58

1 in → 2 out8.1002 XPM226 B

AVqvQJ96…QStXTNs8 AaS74bcc…41H163f3

64b295d0dd8e58…4ce494916c4a1a

1 in → 2 out6.1129 XPM227 B

ALkuPvj3…CrKTc4yG AQXHTLWN…SGHsgNvK

5d17b95c470f03…e5c555608e107a

1 in → 2 out5.1185 XPM227 B

AafXBxi8…MTbj7rvU AK1dGAhb…U3CsLtbu

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.

1.259 × 10⁹³(94-digit number)

12593534965702697534…72781597554459883819

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

1.259 × 10⁹³(94-digit number)

12593534965702697534…72781597554459883819

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.259 × 10⁹³(94-digit number)

12593534965702697534…72781597554459883821

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

2.518 × 10⁹³(94-digit number)

25187069931405395068…45563195108919767639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.518 × 10⁹³(94-digit number)

25187069931405395068…45563195108919767641

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

5.037 × 10⁹³(94-digit number)

50374139862810790137…91126390217839535279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.037 × 10⁹³(94-digit number)

50374139862810790137…91126390217839535281

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

1.007 × 10⁹⁴(95-digit number)

10074827972562158027…82252780435679070559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.007 × 10⁹⁴(95-digit number)

10074827972562158027…82252780435679070561

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

2.014 × 10⁹⁴(95-digit number)

20149655945124316054…64505560871358141119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.014 × 10⁹⁴(95-digit number)

20149655945124316054…64505560871358141121

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