Block #426,788

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/2/2014, 9:56:20 PM · Difficulty 10.3524 · 6,367,610 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1f649d2b95478e9f045594a77235f0962fef7ce659cc50ad90376d5d3a7ca8aa

View on Chainz ↗

Height

#426,788

Difficulty

10.352350

Transactions

Size

899 B

Version

Bits

0a5a33a1

Nonce

494,234

Timestamp

3/2/2014, 9:56:20 PM

Confirmations

6,367,610

Mined by

⛏️ $cliAdFLJFhbQJWBJcv1fjoDef6HbwbsaVkAyh

Merkle Root

959515a2dfbc6df99be172228f8efda56067d1f0abec197fd1cc07452b9c00d5

Transactions (1)

Coinbase959515a2dfbc6d…cc07452b9c00d5

1 in → 22 out9.3200 XPM811 B

AdFLJFhb…bsaVkAyh AcuM7XiJ…5uND8Jce AVRMvm7T…6PC6keBx AZqjMFvv…G8aw2zC8 AH5mD99t…Spv1yg4N

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.

3.156 × 10⁹⁰(91-digit number)

31564313335658325033…69948032766173860479

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

3.156 × 10⁹⁰(91-digit number)

31564313335658325033…69948032766173860479

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.156 × 10⁹⁰(91-digit number)

31564313335658325033…69948032766173860481

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

6.312 × 10⁹⁰(91-digit number)

63128626671316650067…39896065532347720959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.312 × 10⁹⁰(91-digit number)

63128626671316650067…39896065532347720961

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

1.262 × 10⁹¹(92-digit number)

12625725334263330013…79792131064695441919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.262 × 10⁹¹(92-digit number)

12625725334263330013…79792131064695441921

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

2.525 × 10⁹¹(92-digit number)

25251450668526660027…59584262129390883839

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.525 × 10⁹¹(92-digit number)

25251450668526660027…59584262129390883841

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

5.050 × 10⁹¹(92-digit number)

50502901337053320054…19168524258781767679

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.050 × 10⁹¹(92-digit number)

50502901337053320054…19168524258781767681

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