Block #434,112

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/8/2014, 1:35:10 AM · Difficulty 10.3441 · 6,374,900 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7c24788daeed6693996f590b18a82b3cbb71586067bf404b00c3cef2a0df084c

View on Chainz ↗

Height

#434,112

Difficulty

10.344095

Transactions

Size

13.73 KB

Version

Bits

0a58169c

Nonce

15,872

Timestamp

3/8/2014, 1:35:10 AM

Confirmations

6,374,900

Mined by

⛏️ P2SHASxjoE1TgJRCid182iqLk1QscSfFAXiaJP

Merkle Root

17804f13ace9b98c891f87f79fcdfa92b7f4ff9f9268f196bd1cf1d1dba153dd

Transactions (3)

Coinbase8c3e5ab4534cb9…e6bc19b9768767

1 in → 1 out9.4800 XPM109 B

ASxjoE1T…fFAXiaJP

4891a5878a33fc…2c19d6082917ea

6 in → 12 out35.4201 XPM1.18 KB

AWj1CqGp…nomTcpxd APdcbkJa…YJDrWaR3 APaJvQ3G…25PSkPEZ AGaij5dN…mmh48Z5W AezqbyYF…jVCXwRyN

b770421a6bbb5e…8337f240d2c23d

85 in → 2 out31.7488 XPM12.36 KB

AGnqL7Mi…EhDES3fP APKSFkwx…drqDbpup

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.

1.600 × 10⁸⁹(90-digit number)

16005327741374816114…90445084911154668159

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

1.600 × 10⁸⁹(90-digit number)

16005327741374816114…90445084911154668159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.600 × 10⁸⁹(90-digit number)

16005327741374816114…90445084911154668161

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

3.201 × 10⁸⁹(90-digit number)

32010655482749632228…80890169822309336319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.201 × 10⁸⁹(90-digit number)

32010655482749632228…80890169822309336321

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

6.402 × 10⁸⁹(90-digit number)

64021310965499264457…61780339644618672639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.402 × 10⁸⁹(90-digit number)

64021310965499264457…61780339644618672641

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

1.280 × 10⁹⁰(91-digit number)

12804262193099852891…23560679289237345279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.280 × 10⁹⁰(91-digit number)

12804262193099852891…23560679289237345281

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

2.560 × 10⁹⁰(91-digit number)

25608524386199705783…47121358578474690559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.560 × 10⁹⁰(91-digit number)

25608524386199705783…47121358578474690561

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 #434,112

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