Block #372,611

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 5:39:06 PM · Difficulty 10.4271 · 6,436,767 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

9450289d5c4c60d4f05c4b6a50d1d852f6f3f02e3b78845eafd96b7ff471ab8e

View on Chainz ↗

Height

#372,611

Difficulty

10.427062

Transactions

Size

732 B

Version

Bits

0a6d53ec

Nonce

54,406

Timestamp

1/23/2014, 5:39:06 PM

Confirmations

6,436,767

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

acf2153f87a76ee3293a0b8bc85d5beecbe03cab386af38daea9bec4ee023ca0

Transactions (2)

Coinbase396d82481615e2…cb8c5703a8dbb9

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

913ca0547419c2…de0809bc7e140f

3 in → 2 out110.8570 XPM524 B

AKBdQk1b…rpGNAvKs AMrH3mvm…swniVAJK

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.

5.280 × 10⁹⁹(100-digit number)

52809329029917525319…31148324632751308799

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

5.280 × 10⁹⁹(100-digit number)

52809329029917525319…31148324632751308799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.280 × 10⁹⁹(100-digit number)

52809329029917525319…31148324632751308801

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

1.056 × 10¹⁰⁰(101-digit number)

10561865805983505063…62296649265502617599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.056 × 10¹⁰⁰(101-digit number)

10561865805983505063…62296649265502617601

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

2.112 × 10¹⁰⁰(101-digit number)

21123731611967010127…24593298531005235199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.112 × 10¹⁰⁰(101-digit number)

21123731611967010127…24593298531005235201

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

4.224 × 10¹⁰⁰(101-digit number)

42247463223934020255…49186597062010470399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.224 × 10¹⁰⁰(101-digit number)

42247463223934020255…49186597062010470401

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

8.449 × 10¹⁰⁰(101-digit number)

84494926447868040511…98373194124020940799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.449 × 10¹⁰⁰(101-digit number)

84494926447868040511…98373194124020940801

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 #372,611

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