Block #372,617

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 5:49:54 PM · Difficulty 10.4271 · 6,452,151 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2e3002465fe71b866bb3a27d32fc347b3e3434423bc19ebf1fa6cb3cf81a3dfb

View on Chainz ↗

Height

#372,617

Difficulty

10.427072

Transactions

Size

428 B

Version

Bits

0a6d5491

Nonce

20,115

Timestamp

1/23/2014, 5:49:54 PM

Confirmations

6,452,151

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

fec01b18d996df876492fb5ad5d09ab561c9fcc54d4833eb35962e08253710ba

Transactions (2)

Coinbase6f9e438de955d9…d8bd42d42057ad

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

0914ba17dd150a…958b10146329c1

1 in → 2 out7.1015 XPM225 B

AKfzB6km…7op6cNkU AW4jmiGj…4nr8i2me

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.

5.442 × 10¹⁰¹(102-digit number)

54421830903831321657…96868706658581066239

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

5.442 × 10¹⁰¹(102-digit number)

54421830903831321657…96868706658581066239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.442 × 10¹⁰¹(102-digit number)

54421830903831321657…96868706658581066241

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

1.088 × 10¹⁰²(103-digit number)

10884366180766264331…93737413317162132479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.088 × 10¹⁰²(103-digit number)

10884366180766264331…93737413317162132481

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

2.176 × 10¹⁰²(103-digit number)

21768732361532528662…87474826634324264959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.176 × 10¹⁰²(103-digit number)

21768732361532528662…87474826634324264961

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

4.353 × 10¹⁰²(103-digit number)

43537464723065057325…74949653268648529919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.353 × 10¹⁰²(103-digit number)

43537464723065057325…74949653268648529921

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

8.707 × 10¹⁰²(103-digit number)

87074929446130114651…49899306537297059839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.707 × 10¹⁰²(103-digit number)

87074929446130114651…49899306537297059841

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 #372,617

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