Block #150,047

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/4/2013, 6:40:35 PM · Difficulty 9.8583 · 6,660,541 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6fab316fcfb8ee965dd030ced247cad7b94637eb2e732361daa2cdb723eb57d

View on Chainz ↗

Height

#150,047

Difficulty

9.858286

Transactions

Size

722 B

Version

Bits

09dbb89d

Nonce

19,457

Timestamp

9/4/2013, 6:40:35 PM

Confirmations

6,660,541

Mined by

⛏️ P2SHAVbj37YCFJzEtVu5CrKnc84TPZKPBPRuFL

Merkle Root

e61a937f2bc63ec3d2fa296560bf0ac7fb5f87f717ad76cd8701155f49c45ddc

Transactions (2)

Coinbase66a938a2f44dda…5bab9c0c256ebe

1 in → 1 out10.2800 XPM109 B

AVbj37YC…KPBPRuFL

f24c72339685fe…71b72943492947

3 in → 2 out209.4201 XPM522 B

ATr9fboA…4LbjKoQQ ANb8DuSb…GSRbeDNb

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.

2.230 × 10⁹⁶(97-digit number)

22301020917044931192…58404594827021607039

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

2.230 × 10⁹⁶(97-digit number)

22301020917044931192…58404594827021607039

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.230 × 10⁹⁶(97-digit number)

22301020917044931192…58404594827021607041

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

4.460 × 10⁹⁶(97-digit number)

44602041834089862385…16809189654043214079

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.460 × 10⁹⁶(97-digit number)

44602041834089862385…16809189654043214081

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

8.920 × 10⁹⁶(97-digit number)

89204083668179724771…33618379308086428159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.920 × 10⁹⁶(97-digit number)

89204083668179724771…33618379308086428161

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

1.784 × 10⁹⁷(98-digit number)

17840816733635944954…67236758616172856319

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.784 × 10⁹⁷(98-digit number)

17840816733635944954…67236758616172856321

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

3.568 × 10⁹⁷(98-digit number)

35681633467271889908…34473517232345712639

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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 #150,047

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