Block #367,471

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/20/2014, 2:45:03 AM · Difficulty 10.4342 · 6,447,517 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6c927e41939fb7144c9885aff157b21b66ab2e542b2b35e0b7987c6ea426f445

View on Chainz ↗

Height

#367,471

Difficulty

10.434229

Transactions

Size

1.55 KB

Version

Bits

0a6f29a2

Nonce

477,396

Timestamp

1/20/2014, 2:45:03 AM

Confirmations

6,447,517

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

6cdf84753a66f7180c607e2d6eeefebb7fc34702a067a27e96ed5e2471f68f3c

Transactions (3)

Coinbase8da0bb5fe1d797…22b2ea5da3a004

1 in → 1 out9.1900 XPM116 B

AbwWkWZt…kawDhufa

3a7bb8bc76e302…5fd45e9b5c24c5

2 in → 4 out11.0318 XPM406 B

AaKiNte6…LqFxEEHM AMLz4Dj6…KFvw5cVk AeKNrjNj…1NEq95Ta AcacZaAu…7XaX5VD6

02ec10580fa222…8c764e0675498d

6 in → 2 out6.0764 XPM969 B

AV32RiEK…AjWkMMCN ARwz746G…rF6B23pe

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.

3.319 × 10⁹⁹(100-digit number)

33190370062110921843…04752455173740488959

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

3.319 × 10⁹⁹(100-digit number)

33190370062110921843…04752455173740488959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.319 × 10⁹⁹(100-digit number)

33190370062110921843…04752455173740488961

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

6.638 × 10⁹⁹(100-digit number)

66380740124221843686…09504910347480977919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.638 × 10⁹⁹(100-digit number)

66380740124221843686…09504910347480977921

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

1.327 × 10¹⁰⁰(101-digit number)

13276148024844368737…19009820694961955839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.327 × 10¹⁰⁰(101-digit number)

13276148024844368737…19009820694961955841

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

2.655 × 10¹⁰⁰(101-digit number)

26552296049688737474…38019641389923911679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.655 × 10¹⁰⁰(101-digit number)

26552296049688737474…38019641389923911681

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

5.310 × 10¹⁰⁰(101-digit number)

53104592099377474949…76039282779847823359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.310 × 10¹⁰⁰(101-digit number)

53104592099377474949…76039282779847823361

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 #367,471

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