Block #462,041

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/27/2014, 4:19:19 AM · Difficulty 10.4109 · 6,342,233 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e73b5ed05c9c2264e68d551fc6e3e9de52006e9c159a786c3876432c3fe3b251

View on Chainz ↗

Height

#462,041

Difficulty

10.410939

Transactions

Size

628 B

Version

Bits

0a693346

Nonce

64,281

Timestamp

3/27/2014, 4:19:19 AM

Confirmations

6,342,233

Mined by

⛏️ P2SHAX1o6FDB9LS9K46N2dSB1yGQfoiPZfBFvw

Merkle Root

5775d74c85699cdc3bc0a89b3e33a984d4be296568c26ffed43b3094a78e0dfa

Transactions (2)

Coinbase6950bcf113290d…e68ddbbfd04cea

1 in → 1 out9.2200 XPM109 B

AX1o6FDB…iPZfBFvw

5113f9c02d4f9b…958702d0708b0c

1 in → 9 out9.1800 XPM430 B

AKFGoz2z…5A25kyka AQv2iMwd…EFna22ee ASY5xqVU…DNRfWDXj AT6V8ebA…kxfTNYPW AU9KdB9r…o5XC6WMy

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.

8.613 × 10⁹²(93-digit number)

86131778926419334935…46818368366794264319

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

8.613 × 10⁹²(93-digit number)

86131778926419334935…46818368366794264319

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.613 × 10⁹²(93-digit number)

86131778926419334935…46818368366794264321

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

1.722 × 10⁹³(94-digit number)

17226355785283866987…93636736733588528639

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.722 × 10⁹³(94-digit number)

17226355785283866987…93636736733588528641

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

3.445 × 10⁹³(94-digit number)

34452711570567733974…87273473467177057279

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.445 × 10⁹³(94-digit number)

34452711570567733974…87273473467177057281

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

6.890 × 10⁹³(94-digit number)

68905423141135467948…74546946934354114559

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.890 × 10⁹³(94-digit number)

68905423141135467948…74546946934354114561

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

1.378 × 10⁹⁴(95-digit number)

13781084628227093589…49093893868708229119

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.378 × 10⁹⁴(95-digit number)

13781084628227093589…49093893868708229121

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