Block #373,674

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/24/2014, 11:45:58 AM · Difficulty 10.4245 · 6,438,634 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

427c7eca30e1b532d2e3208346a72bbea1c387b0a3e62b9d4fda6ea62dd03927

View on Chainz ↗

Height

#373,674

Difficulty

10.424510

Transactions

Size

435 B

Version

Bits

0a6cacb6

Nonce

61,586

Timestamp

1/24/2014, 11:45:58 AM

Confirmations

6,438,634

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e98eef34b2860290ccc9c05f8070e46e4bfb437710a465bdf77a168f07149763

Transactions (2)

Coinbase6c67fafd0eb480…02bbddf52bc691

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

cf187cd3ed424d…6f99dd442abcf4

1 in → 2 out5.0542 XPM227 B

AZd1QKGr…xRh87nqw AN6URKxg…7mwfYRWU

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.

1.212 × 10⁹⁹(100-digit number)

12126308399215854317…65410202485834054399

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

1.212 × 10⁹⁹(100-digit number)

12126308399215854317…65410202485834054399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.212 × 10⁹⁹(100-digit number)

12126308399215854317…65410202485834054401

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

2.425 × 10⁹⁹(100-digit number)

24252616798431708635…30820404971668108799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.425 × 10⁹⁹(100-digit number)

24252616798431708635…30820404971668108801

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

4.850 × 10⁹⁹(100-digit number)

48505233596863417271…61640809943336217599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.850 × 10⁹⁹(100-digit number)

48505233596863417271…61640809943336217601

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

9.701 × 10⁹⁹(100-digit number)

97010467193726834542…23281619886672435199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.701 × 10⁹⁹(100-digit number)

97010467193726834542…23281619886672435201

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

1.940 × 10¹⁰⁰(101-digit number)

19402093438745366908…46563239773344870399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.940 × 10¹⁰⁰(101-digit number)

19402093438745366908…46563239773344870401

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 #373,674

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