Block #375,988

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 2:45:19 AM · Difficulty 10.4224 · 6,433,257 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2d934970a9e9a07efa74e4b47053d522a2c349188756fb53fb4f6b534a7dd1c6

View on Chainz ↗

Height

#375,988

Difficulty

10.422435

Transactions

Size

1.09 KB

Version

Bits

0a6c24ad

Nonce

8,699

Timestamp

1/26/2014, 2:45:19 AM

Confirmations

6,433,257

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

e3a971cbad1f98602594aceae236fe19419fefebf7e540e93b77e6e980bb0f2c

Transactions (5)

Coinbase416943d42c94fa…db0d4cf8aa0271

1 in → 1 out9.2300 XPM116 B

AbwWkWZt…kawDhufa

d017e95784191d…6d4a7759e075c9

1 in → 2 out4240.7124 XPM227 B

AUH3xfYy…nRACEc38 AP7WvdQE…sSZF2sQ4

4f66dcd95efba5…f7dc6d7c27b0e0

1 in → 2 out8.1595 XPM226 B

AajaLDZz…nAgjJngQ ANHneJGq…7GgCBRk7

b914cfbb9204e6…d678ec2951c905

1 in → 2 out7.1279 XPM225 B

AWi9sFLX…xENWPVEb ARBo3mrR…ChB1pPoQ

98a330a89a83e9…bb17350734ee1f

1 in → 2 out2.0575 XPM226 B

AKUEaUvA…6nAqWbP5 ANdN3HiR…PPm72GdB

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.

9.083 × 10¹⁰¹(102-digit number)

90830825501720471275…90296741853237084159

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

9.083 × 10¹⁰¹(102-digit number)

90830825501720471275…90296741853237084159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.083 × 10¹⁰¹(102-digit number)

90830825501720471275…90296741853237084161

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

1.816 × 10¹⁰²(103-digit number)

18166165100344094255…80593483706474168319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.816 × 10¹⁰²(103-digit number)

18166165100344094255…80593483706474168321

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

3.633 × 10¹⁰²(103-digit number)

36332330200688188510…61186967412948336639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.633 × 10¹⁰²(103-digit number)

36332330200688188510…61186967412948336641

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

7.266 × 10¹⁰²(103-digit number)

72664660401376377020…22373934825896673279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.266 × 10¹⁰²(103-digit number)

72664660401376377020…22373934825896673281

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

1.453 × 10¹⁰³(104-digit number)

14532932080275275404…44747869651793346559

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.453 × 10¹⁰³(104-digit number)

14532932080275275404…44747869651793346561

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 #375,988

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