Block #423,725

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 2/28/2014, 3:05:56 PM · Difficulty 10.3790 · 6,403,033 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

13bc8355f24ff0e00903550ba9b723cd775088876cfd7ec50efce8401ea4f7b4

View on Chainz ↗

Height

#423,725

Difficulty

10.379017

Transactions

Size

2.04 KB

Version

Bits

0a610741

Nonce

141,646

Timestamp

2/28/2014, 3:05:56 PM

Confirmations

6,403,033

Mined by

⛏️ -wAMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

ea2b5ed53e0c8ef0dda6b3f05d698da415bb23dea8489d89a0d70e4f4ac61a03

Transactions (4)

Coinbase8f88b4cc352fad…c1b8c96160dc96

1 in → 2 out9.3100 XPM131 B

AMVf7Jrg…xd5AVR7C AJno7LX2…vo4wdWtY

541778e7464d9b…fdac17c67497ad

6 in → 17 out55.7500 XPM1.24 KB

AcHBUwAj…VfZUHxc8 AGvwvYXM…1kPKkTkQ AbeK2fRg…y6tUksG7 AevYewTX…WvBtzTFH AdTtZYv4…mEzssnpx

a6669520a5b6aa…fa35b87c780c7a

1 in → 2 out5.1196 XPM225 B

AcR8FEH2…LeiqouRM AQ4E5dVv…piwKULtE

1b185ca285dc80…fd6ab3635b3b40

2 in → 2 out1.0472 XPM373 B

Acd9QzkX…HerMkUNx AMBQCSV3…ag8AGGp5

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.

9.972 × 10⁹³(94-digit number)

99723799208960987275…65906302456331273999

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

9.972 × 10⁹³(94-digit number)

99723799208960987275…65906302456331273999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.972 × 10⁹³(94-digit number)

99723799208960987275…65906302456331274001

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

1.994 × 10⁹⁴(95-digit number)

19944759841792197455…31812604912662547999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.994 × 10⁹⁴(95-digit number)

19944759841792197455…31812604912662548001

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

3.988 × 10⁹⁴(95-digit number)

39889519683584394910…63625209825325095999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.988 × 10⁹⁴(95-digit number)

39889519683584394910…63625209825325096001

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

7.977 × 10⁹⁴(95-digit number)

79779039367168789820…27250419650650191999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.977 × 10⁹⁴(95-digit number)

79779039367168789820…27250419650650192001

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

1.595 × 10⁹⁵(96-digit number)

15955807873433757964…54500839301300383999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.595 × 10⁹⁵(96-digit number)

15955807873433757964…54500839301300384001

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 #423,725

Cookie Preferences