Block #331,883

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 12/27/2013, 3:54:14 PM · Difficulty 10.1740 · 6,486,049 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a63b8dbef04ebfcfcb3a0fff1740a57a879138b0c773809071776b8a8eadd8bf

View on Chainz ↗

Height

#331,883

Difficulty

10.173983

Transactions

Size

951 B

Version

Bits

0a2c8a26

Nonce

44,177

Timestamp

12/27/2013, 3:54:14 PM

Confirmations

6,486,049

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c126829ab2770ad0d491a5b057072eec5d9af2cca070d1f8ab1f5c8ff654f8fa

Transactions (3)

Coinbasef59a376df0088d…35095b237709cd

1 in → 1 out9.6700 XPM110 B

AeKNrjNj…1NEq95Ta

6b439373d834d8…b04e27581a5eb2

2 in → 2 out1.1358 XPM374 B

ARTcaCVH…LMYVgsg5 AaM5pXGr…CmtPdCpb

0ee3aa8e63839b…3249be04165fcf

2 in → 2 out1.0263 XPM375 B

AUAfYcmQ…B3DywuZK AcgPtMbN…urvUQ4E4

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.

1.235 × 10⁹⁹(100-digit number)

12351228313259541772…70327134162175329279

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

1.235 × 10⁹⁹(100-digit number)

12351228313259541772…70327134162175329279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.235 × 10⁹⁹(100-digit number)

12351228313259541772…70327134162175329281

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

2.470 × 10⁹⁹(100-digit number)

24702456626519083545…40654268324350658559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.470 × 10⁹⁹(100-digit number)

24702456626519083545…40654268324350658561

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

4.940 × 10⁹⁹(100-digit number)

49404913253038167091…81308536648701317119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.940 × 10⁹⁹(100-digit number)

49404913253038167091…81308536648701317121

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

9.880 × 10⁹⁹(100-digit number)

98809826506076334183…62617073297402634239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.880 × 10⁹⁹(100-digit number)

98809826506076334183…62617073297402634241

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

1.976 × 10¹⁰⁰(101-digit number)

19761965301215266836…25234146594805268479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.976 × 10¹⁰⁰(101-digit number)

19761965301215266836…25234146594805268481

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 #331,883

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