Block #426,663

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 7:10:17 PM · Difficulty 10.3569 · 6,367,867 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e571e75b04e8d7cf6ff28efe4639720af9341fc6f25062be4f1353bd3d794410

View on Chainz ↗

Height

#426,663

Difficulty

10.356865

Transactions

Size

560 B

Version

Bits

0a5b5b7f

Nonce

26,147

Timestamp

3/2/2014, 7:10:17 PM

Confirmations

6,367,867

Mined by

⛏️ aSAWQBKr3YBNqdknh157YGqdQEjQsUA1Ehpd

Merkle Root

88ec8003fde9f11ecd5a9f73f224d99d985b63cf8f95f2a427c216300a5dee26

Transactions (2)

Coinbase57b97202345ea6…dae0926ee12748

1 in → 1 out9.3100 XPM97 B

AWQBKr3Y…sUA1Ehpd

3dbea6952326ad…15b5f4d4bf5b74

2 in → 2 out40.2681 XPM374 B

AGhqx9U2…jxFM6Bm6 AFpnUwMG…QKjGA3z1

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.

1.331 × 10⁹³(94-digit number)

13316994631988907835…10410243602873039999

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

1.331 × 10⁹³(94-digit number)

13316994631988907835…10410243602873039999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.331 × 10⁹³(94-digit number)

13316994631988907835…10410243602873040001

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

2.663 × 10⁹³(94-digit number)

26633989263977815671…20820487205746079999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.663 × 10⁹³(94-digit number)

26633989263977815671…20820487205746080001

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

5.326 × 10⁹³(94-digit number)

53267978527955631343…41640974411492159999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.326 × 10⁹³(94-digit number)

53267978527955631343…41640974411492160001

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

1.065 × 10⁹⁴(95-digit number)

10653595705591126268…83281948822984319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.065 × 10⁹⁴(95-digit number)

10653595705591126268…83281948822984320001

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

2.130 × 10⁹⁴(95-digit number)

21307191411182252537…66563897645968639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.130 × 10⁹⁴(95-digit number)

21307191411182252537…66563897645968640001

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