Block #376,883

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/26/2014, 5:11:41 PM · Difficulty 10.4259 · 6,426,540 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e3876fe72feaf7d81f5c5a90e17a6e90670528582434d359b2be3fce13319bfd

View on Chainz ↗

Height

#376,883

Difficulty

10.425925

Transactions

Size

869 B

Version

Bits

0a6d0965

Nonce

11,063

Timestamp

1/26/2014, 5:11:41 PM

Confirmations

6,426,540

Mined by

⛏️ 3aRA#AbMAHMS8edmSw9jhkJ2fCCZzvKMwEzMSoj

Merkle Root

25264c807be1c536247741d9864e528869099beea6492d7488f16eac327f82a5

Transactions (4)

Coinbasec19510569b32cc…052948221c641d

1 in → 1 out9.1900 XPM97 B

AbMAHMS8…MwEzMSoj

e636a45d8c2745…04e0672ed28ac3

1 in → 2 out9.1700 XPM227 B

ALC6zrBD…beXNtJBJ AK6J7HBH…RZ8Xdg95

b61b3779b3798b…41114a3e434ef6

1 in → 2 out9.1700 XPM227 B

AYHYC1Uc…DhPftv6g AVVvVC2v…ByPnMRtd

a3eb3f5febc32d…5a28c66c09dddc

1 in → 2 out8.1544 XPM226 B

AMJDChGB…VXxUjXFK Aewc1hUb…n71JNgRP

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.

2.077 × 10⁹⁹(100-digit number)

20774707576450531419…93482277706696560639

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

2.077 × 10⁹⁹(100-digit number)

20774707576450531419…93482277706696560639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.077 × 10⁹⁹(100-digit number)

20774707576450531419…93482277706696560641

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

4.154 × 10⁹⁹(100-digit number)

41549415152901062838…86964555413393121279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.154 × 10⁹⁹(100-digit number)

41549415152901062838…86964555413393121281

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

8.309 × 10⁹⁹(100-digit number)

83098830305802125677…73929110826786242559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.309 × 10⁹⁹(100-digit number)

83098830305802125677…73929110826786242561

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

1.661 × 10¹⁰⁰(101-digit number)

16619766061160425135…47858221653572485119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.661 × 10¹⁰⁰(101-digit number)

16619766061160425135…47858221653572485121

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

3.323 × 10¹⁰⁰(101-digit number)

33239532122320850271…95716443307144970239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.323 × 10¹⁰⁰(101-digit number)

33239532122320850271…95716443307144970241

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