Block #375,658

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/25/2014, 8:59:03 PM · Difficulty 10.4243 · 6,462,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

66ddab0f6efa0f42286810ccf52d13711b2da1884b4c85caeb2f5a1964d0d8f3

View on Chainz ↗

Height

#375,658

Difficulty

10.424265

Transactions

Size

1.08 KB

Version

Bits

0a6c9ca7

Nonce

10,684

Timestamp

1/25/2014, 8:59:03 PM

Confirmations

6,462,517

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

fa1f588d97cb39ca1d17402a1ad7046167dab112b2706d65004e65fa700a1b40

Transactions (5)

Coinbase245cae3675e392…e4b6206fabdb43

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

dd3e6da00d9b08…fd057c54354c84

1 in → 2 out8.1466 XPM225 B

AXHPBfqY…NbieHvJ3 ATiP2myP…qVUH8Grb

175f350b632fcd…1bfdc2350634f6

1 in → 2 out8.1450 XPM225 B

AUDqnJmw…dUnnehQc AZCTjBAd…nYsqV2eZ

f6a64f84a34a22…1c7d814ef20802

1 in → 2 out4.1371 XPM225 B

AXzcLJ3G…Xb9MEjb4 AaVFHFSq…bCnX1Bpw

be9197a0f5ab36…339251ee06e996

1 in → 2 out8.1475 XPM226 B

AZxQXAk2…3kdaYb1Y AdEKgi3R…kMFCH4zP

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.

1.482 × 10¹⁰³(104-digit number)

14820813902837120425…15955816505375513749

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

1.482 × 10¹⁰³(104-digit number)

14820813902837120425…15955816505375513749

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.482 × 10¹⁰³(104-digit number)

14820813902837120425…15955816505375513751

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

2.964 × 10¹⁰³(104-digit number)

29641627805674240851…31911633010751027499

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.964 × 10¹⁰³(104-digit number)

29641627805674240851…31911633010751027501

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

5.928 × 10¹⁰³(104-digit number)

59283255611348481703…63823266021502054999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.928 × 10¹⁰³(104-digit number)

59283255611348481703…63823266021502055001

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

1.185 × 10¹⁰⁴(105-digit number)

11856651122269696340…27646532043004109999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.185 × 10¹⁰⁴(105-digit number)

11856651122269696340…27646532043004110001

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

2.371 × 10¹⁰⁴(105-digit number)

23713302244539392681…55293064086008219999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.371 × 10¹⁰⁴(105-digit number)

23713302244539392681…55293064086008220001

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 #375,658

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