Block #377,929

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/27/2014, 11:26:04 AM · Difficulty 10.4205 · 6,426,080 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb04ba0bd75a15b3418b6ca9c7d2f2b152e1d7d19ea62c4df7ee6410f5e4a92a

View on Chainz ↗

Height

#377,929

Difficulty

10.420517

Transactions

Size

583 B

Version

Bits

0a6ba6fb

Nonce

35,205

Timestamp

1/27/2014, 11:26:04 AM

Confirmations

6,426,080

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

22a1fcda3bc21376542c0674480d2a1b61a1134ef2e06c2e1b41a2445cda4f5c

Transactions (2)

Coinbase34742a1baac43a…660d14cf432f56

1 in → 1 out9.2000 XPM116 B

AbwWkWZt…kawDhufa

335f10fc745821…91c0ec130a5daf

2 in → 2 out499.9100 XPM374 B

AVwQuDSr…KsE1rjJF AXKgE1pw…DBuxBWoK

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.

1.129 × 10¹⁰¹(102-digit number)

11295371512739267930…08772451827417702399

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

1.129 × 10¹⁰¹(102-digit number)

11295371512739267930…08772451827417702399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.129 × 10¹⁰¹(102-digit number)

11295371512739267930…08772451827417702401

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

2.259 × 10¹⁰¹(102-digit number)

22590743025478535861…17544903654835404799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.259 × 10¹⁰¹(102-digit number)

22590743025478535861…17544903654835404801

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

4.518 × 10¹⁰¹(102-digit number)

45181486050957071723…35089807309670809599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.518 × 10¹⁰¹(102-digit number)

45181486050957071723…35089807309670809601

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

9.036 × 10¹⁰¹(102-digit number)

90362972101914143446…70179614619341619199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.036 × 10¹⁰¹(102-digit number)

90362972101914143446…70179614619341619201

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

1.807 × 10¹⁰²(103-digit number)

18072594420382828689…40359229238683238399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.807 × 10¹⁰²(103-digit number)

18072594420382828689…40359229238683238401

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