Block #370,513

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/22/2014, 4:59:23 AM · Difficulty 10.4380 · 6,437,058 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a22c26516ecb92afccb3bffd6b7222c11399d22700befa107d51a8560a39b29d

View on Chainz ↗

Height

#370,513

Difficulty

10.437979

Transactions

Size

666 B

Version

Bits

0a701f64

Nonce

8,982

Timestamp

1/22/2014, 4:59:23 AM

Confirmations

6,437,058

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

22479f219e03b0d022046e621408584be4d09e3c52482af9168e65f3887a9060

Transactions (3)

Coinbase54980308595f1b…f2ddcf687d4d96

1 in → 1 out9.1800 XPM116 B

AbwWkWZt…kawDhufa

a05a616e773467…0c346615e7dc79

1 in → 2 out8.1060 XPM227 B

AaokDHoa…zdVui1kd AHBPDLPB…smEr98yf

3f8ae7595fe7e0…00355b8e9eedb1

1 in → 2 out8.0357 XPM227 B

AVCXQFU9…ndSyK98w AGMMN4Uo…Vmgi8Kei

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.

4.572 × 10¹⁰⁹(110-digit number)

45722131025863688398…07682563351605515519

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

4.572 × 10¹⁰⁹(110-digit number)

45722131025863688398…07682563351605515519

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.572 × 10¹⁰⁹(110-digit number)

45722131025863688398…07682563351605515521

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

9.144 × 10¹⁰⁹(110-digit number)

91444262051727376797…15365126703211031039

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.144 × 10¹⁰⁹(110-digit number)

91444262051727376797…15365126703211031041

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

1.828 × 10¹¹⁰(111-digit number)

18288852410345475359…30730253406422062079

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.828 × 10¹¹⁰(111-digit number)

18288852410345475359…30730253406422062081

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

3.657 × 10¹¹⁰(111-digit number)

36577704820690950718…61460506812844124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.657 × 10¹¹⁰(111-digit number)

36577704820690950718…61460506812844124161

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

7.315 × 10¹¹⁰(111-digit number)

73155409641381901437…22921013625688248319

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.315 × 10¹¹⁰(111-digit number)

73155409641381901437…22921013625688248321

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 #370,513

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