Block #372,464

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/23/2014, 3:05:40 PM · Difficulty 10.4278 · 6,437,991 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

96f322a81b6cdc45c911266bb3956a473c46e384c8b0a219558ff5e13aec06f5

View on Chainz ↗

Height

#372,464

Difficulty

10.427775

Transactions

Size

1.28 KB

Version

Bits

0a6d82b0

Nonce

65,088

Timestamp

1/23/2014, 3:05:40 PM

Confirmations

6,437,991

Mined by

⛏️ P2SHAQo5Sf84DcjUC65gbiaUvY1LDSCktZTnkR

Merkle Root

9537816f3e9dbaaea67c367c4e369f1dda524d5c90c2b6f4c751bfd725e82e9f

Transactions (3)

Coinbasef3097154480db5…26eb2a27bcd9e3

1 in → 1 out9.2000 XPM109 B

AQo5Sf84…CktZTnkR

34a6d9b9103304…3c6b9d0e807eb6

4 in → 2 out8.0100 XPM671 B

AGhK9uxx…eMYnZfLE AU3haE96…pgdnHyvg

d3aa270a0dee9b…20c83a24e8404e

2 in → 5 out14.6444 XPM442 B

AeKNrjNj…1NEq95Ta AXwqbhta…JjFBYZxR ALrZxq5u…jReX3z9e ALvVMKLt…wbxp4TJH AeYjcQm6…JX7NwXHM

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.

3.693 × 10⁹⁶(97-digit number)

36939820664237752487…10351484232042895359

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

3.693 × 10⁹⁶(97-digit number)

36939820664237752487…10351484232042895359

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.693 × 10⁹⁶(97-digit number)

36939820664237752487…10351484232042895361

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

7.387 × 10⁹⁶(97-digit number)

73879641328475504975…20702968464085790719

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.387 × 10⁹⁶(97-digit number)

73879641328475504975…20702968464085790721

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

1.477 × 10⁹⁷(98-digit number)

14775928265695100995…41405936928171581439

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.477 × 10⁹⁷(98-digit number)

14775928265695100995…41405936928171581441

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

2.955 × 10⁹⁷(98-digit number)

29551856531390201990…82811873856343162879

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.955 × 10⁹⁷(98-digit number)

29551856531390201990…82811873856343162881

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

5.910 × 10⁹⁷(98-digit number)

59103713062780403980…65623747712686325759

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.910 × 10⁹⁷(98-digit number)

59103713062780403980…65623747712686325761

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 #372,464

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