Block #372,230

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 10:59:55 AM · Difficulty 10.4290 · 6,435,390 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0a06990aa5c86f7698195e6ec99e04be443d705a0f48d674f44bc6b33d113177

View on Chainz ↗

Height

#372,230

Difficulty

10.429008

Transactions

Size

888 B

Version

Bits

0a6dd37d

Nonce

33,081

Timestamp

1/23/2014, 10:59:55 AM

Confirmations

6,435,390

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

7720c2cf9a8ff1cd3a1040e7be137d1364244325ce5294b1ac3faefd3a88b72d

Transactions (4)

Coinbasece24e8132ad8de…cdf90553b193ed

1 in → 1 out9.2200 XPM116 B

AbwWkWZt…kawDhufa

46ea03e0fe8be3…9ba12587158010

1 in → 2 out3.0077 XPM226 B

AMt7ReCs…GSTPE2pE AcDZWWfG…4YdR7GSH

8dd563863145c0…5dab5f37a42f18

1 in → 2 out1.0694 XPM226 B

AdgmqJRT…xfd5jWGs AJS89izG…wQ8MNDp3

bc35bf24171791…b33474b542bf1b

1 in → 2 out3.0281 XPM227 B

ATY8fqeh…M8FEFqDP ARtYftjF…RZKJQ3ey

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.

7.817 × 10¹⁰⁰(101-digit number)

78173910730196856401…80512558122580402809

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

7.817 × 10¹⁰⁰(101-digit number)

78173910730196856401…80512558122580402809

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.817 × 10¹⁰⁰(101-digit number)

78173910730196856401…80512558122580402811

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

1.563 × 10¹⁰¹(102-digit number)

15634782146039371280…61025116245160805619

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.563 × 10¹⁰¹(102-digit number)

15634782146039371280…61025116245160805621

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

3.126 × 10¹⁰¹(102-digit number)

31269564292078742560…22050232490321611239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.126 × 10¹⁰¹(102-digit number)

31269564292078742560…22050232490321611241

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

6.253 × 10¹⁰¹(102-digit number)

62539128584157485121…44100464980643222479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.253 × 10¹⁰¹(102-digit number)

62539128584157485121…44100464980643222481

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

1.250 × 10¹⁰²(103-digit number)

12507825716831497024…88200929961286444959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.250 × 10¹⁰²(103-digit number)

12507825716831497024…88200929961286444961

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 #372,230

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