Block #224,515

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/23/2013, 7:58:11 PM · Difficulty 9.9370 · 6,602,673 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4412fdd95e84997b438254fae953b22844bb646f7e5394f9a0abcf0e9cbe44dd

View on Chainz ↗

Height

#224,515

Difficulty

9.937026

Transactions

Size

4.97 KB

Version

Bits

09efe0f7

Nonce

31,857

Timestamp

10/23/2013, 7:58:11 PM

Confirmations

6,602,673

Mined by

⛏️ P2SHAeZgWM4uLXMf754SKWwvFsuqY8N8m9HDRy

Merkle Root

72478c8bf8e5995e728e581c6a640ecda8866ca6c3a176c171fe8494ca413eb6

Transactions (3)

Coinbase3e8fdecc9650f4…bd638b31cf0634

1 in → 1 out10.1600 XPM109 B

AeZgWM4u…N8m9HDRy

8aa8dcf44fe986…e077db2704d07f

6 in → 2 out267.9000 XPM965 B

ARFLfJzn…WKH1hZfS Ac7RAQMV…nKWU2GLU

fe9dceba040457…e23f309e783798

26 in → 2 out4.3586 XPM3.83 KB

ALWXFgY4…BH8CfEcq AM1BC8ii…puFJeaYa

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.

1.922 × 10⁹³(94-digit number)

19220492890431152207…87706214031847259199

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

1.922 × 10⁹³(94-digit number)

19220492890431152207…87706214031847259199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.922 × 10⁹³(94-digit number)

19220492890431152207…87706214031847259201

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

3.844 × 10⁹³(94-digit number)

38440985780862304415…75412428063694518399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.844 × 10⁹³(94-digit number)

38440985780862304415…75412428063694518401

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

7.688 × 10⁹³(94-digit number)

76881971561724608831…50824856127389036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.688 × 10⁹³(94-digit number)

76881971561724608831…50824856127389036801

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

1.537 × 10⁹⁴(95-digit number)

15376394312344921766…01649712254778073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.537 × 10⁹⁴(95-digit number)

15376394312344921766…01649712254778073601

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

3.075 × 10⁹⁴(95-digit number)

30752788624689843532…03299424509556147199

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 #224,515

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