Block #374,998

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 10:33:45 AM · Difficulty 10.4201 · 6,440,126 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5452f1f6731c80d56f129ef7910741b0cf8ca3ce26fb418a81893c04b5be975f

View on Chainz ↗

Height

#374,998

Difficulty

10.420141

Transactions

Size

1.09 KB

Version

Bits

0a6b8e5c

Nonce

5,343

Timestamp

1/25/2014, 10:33:45 AM

Confirmations

6,440,126

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

3d775061181769d442a64fbe1031962ccd2eaffa3d65fe217b959215780ebf3a

Transactions (5)

Coinbase855eb7f24a732e…3eb0b913e24aa6

1 in → 1 out9.2400 XPM116 B

AbwWkWZt…kawDhufa

5e2f9294d3a052…650cee23327121

1 in → 2 out9.1600 XPM226 B

ANq32YwQ…5Azp5nDr ASfQj9Pb…Q87HBF2g

3b511caf5ea1ff…7f81ee73b30b17

1 in → 2 out9.1600 XPM227 B

AUokv8rQ…P533yV4u AdLUwXXn…8DQyVgf7

3b402c04bce1db…ac04937ec9a27b

1 in → 2 out6.1170 XPM227 B

ALH4zVz9…GcohduH8 AetMuNgb…n2wdbLdd

90fe7d95f87206…6d2473c1fe8258

1 in → 2 out4.0844 XPM226 B

ALTPsn6w…R5zEUhq4 AWZcpbCB…2t2PoGkJ

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.

7.583 × 10¹⁰³(104-digit number)

75837124633675437287…07628969614130544639

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

7.583 × 10¹⁰³(104-digit number)

75837124633675437287…07628969614130544639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.583 × 10¹⁰³(104-digit number)

75837124633675437287…07628969614130544641

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

1.516 × 10¹⁰⁴(105-digit number)

15167424926735087457…15257939228261089279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.516 × 10¹⁰⁴(105-digit number)

15167424926735087457…15257939228261089281

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

3.033 × 10¹⁰⁴(105-digit number)

30334849853470174914…30515878456522178559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.033 × 10¹⁰⁴(105-digit number)

30334849853470174914…30515878456522178561

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

6.066 × 10¹⁰⁴(105-digit number)

60669699706940349829…61031756913044357119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.066 × 10¹⁰⁴(105-digit number)

60669699706940349829…61031756913044357121

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

1.213 × 10¹⁰⁵(106-digit number)

12133939941388069965…22063513826088714239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.213 × 10¹⁰⁵(106-digit number)

12133939941388069965…22063513826088714241

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 #374,998

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