Block #376,938

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 6:14:32 PM · Difficulty 10.4250 · 6,418,055 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6a955ca412edc1e9a8dac572546884d265bc655f13bd39e590602292a5db82d4

View on Chainz ↗

Height

#376,938

Difficulty

10.425023

Transactions

Size

433 B

Version

Bits

0a6cce57

Nonce

117,441,629

Timestamp

1/26/2014, 6:14:32 PM

Confirmations

6,418,055

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

61900f4b4762407b2cdd9e943cbee8ab87979a3812fd67bd77d51d5a4eb2d4c1

Transactions (2)

Coinbasec14bf8a0fcbcec…50a2c3da2dd7e3

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

007f771789fb4f…3cba391a8c60d6

1 in → 2 out8.1599 XPM226 B

AaHoq7LW…kCQuDAF4 AWuLNcCP…Lisgn5ry

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.

5.763 × 10⁹⁶(97-digit number)

57632126914514427921…44280609271137484799

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

5.763 × 10⁹⁶(97-digit number)

57632126914514427921…44280609271137484799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.763 × 10⁹⁶(97-digit number)

57632126914514427921…44280609271137484801

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

1.152 × 10⁹⁷(98-digit number)

11526425382902885584…88561218542274969599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.152 × 10⁹⁷(98-digit number)

11526425382902885584…88561218542274969601

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

2.305 × 10⁹⁷(98-digit number)

23052850765805771168…77122437084549939199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.305 × 10⁹⁷(98-digit number)

23052850765805771168…77122437084549939201

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

4.610 × 10⁹⁷(98-digit number)

46105701531611542336…54244874169099878399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.610 × 10⁹⁷(98-digit number)

46105701531611542336…54244874169099878401

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

9.221 × 10⁹⁷(98-digit number)

92211403063223084673…08489748338199756799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.221 × 10⁹⁷(98-digit number)

92211403063223084673…08489748338199756801

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