Block #243,123

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/4/2013, 3:03:13 AM · Difficulty 9.9610 · 6,563,162 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16f61f6a641b319337170dddc147f5f510336c4f56a53513dfb8a4a0f7de790e

View on Chainz ↗

Height

#243,123

Difficulty

9.961034

Transactions

Size

948 B

Version

Bits

09f60653

Nonce

124,206

Timestamp

11/4/2013, 3:03:13 AM

Confirmations

6,563,162

Mined by

⛏️ P2SHAPKpsm65Uq2fyRWqMXs4ycWvQc7AGVvHko

Merkle Root

40da2351e4e68063b02fd8e71a60c1b4bafe66214abc9b7d45971020692d9857

Transactions (3)

Coinbase454a7464f8ebc7…13d854eeaebc6c

1 in → 1 out10.0800 XPM109 B

APKpsm65…7AGVvHko

b079b19bb818f0…1deb88bcb83b34

1 in → 1 out10.0900 XPM159 B

ASaFMDru…mJexLBEv

6f991296c1e7b1…837de83eb45ee1

3 in → 6 out20.4807 XPM590 B

AeKNrjNj…1NEq95Ta AdBg5KBk…HQqjgCFj AUzJmR9P…haHdgAyg AUDB1fin…mSCsqMVN Ae38JbMC…RPmPs1eS

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.

8.494 × 10⁹⁴(95-digit number)

84942437688360600090…19093224415505194239

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

8.494 × 10⁹⁴(95-digit number)

84942437688360600090…19093224415505194239

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.494 × 10⁹⁴(95-digit number)

84942437688360600090…19093224415505194241

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

1.698 × 10⁹⁵(96-digit number)

16988487537672120018…38186448831010388479

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.698 × 10⁹⁵(96-digit number)

16988487537672120018…38186448831010388481

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

3.397 × 10⁹⁵(96-digit number)

33976975075344240036…76372897662020776959

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.397 × 10⁹⁵(96-digit number)

33976975075344240036…76372897662020776961

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

6.795 × 10⁹⁵(96-digit number)

67953950150688480072…52745795324041553919

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.795 × 10⁹⁵(96-digit number)

67953950150688480072…52745795324041553921

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

1.359 × 10⁹⁶(97-digit number)

13590790030137696014…05491590648083107839

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.359 × 10⁹⁶(97-digit number)

13590790030137696014…05491590648083107841

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 #243,123

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