Block #23,204

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 7:23:26 PM · Difficulty 7.9580 · 6,781,815 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f6b7007d0371dacfcbd1e4b75cbbf4e00864f90098d7eef4f3c970c065663762

View on Chainz ↗

Height

#23,204

Difficulty

7.957996

Transactions

Size

357 B

Version

Bits

07f53f3d

Nonce

Timestamp

7/12/2013, 7:23:26 PM

Confirmations

6,781,815

Mined by

⛏️ P2SHALXjrugCYbt29xU2ER2ywowb9GhByoynjy

Merkle Root

6b7e3569d485f961d83068f2cff78f2741a1928e97399a5dce631fbfc8bd56f6

Transactions (2)

Coinbasea3182fd44a2abd…09e8699ac6e3de

1 in → 1 out15.7800 XPM109 B

ALXjrugC…hByoynjy

18a988e40b778d…fda42d240f4c97

1 in → 1 out15.8800 XPM159 B

Abh4rSGH…pjZ7VPMu

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.

1.116 × 10⁹³(94-digit number)

11168282802932413292…37840536963661180979

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

1.116 × 10⁹³(94-digit number)

11168282802932413292…37840536963661180979

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.116 × 10⁹³(94-digit number)

11168282802932413292…37840536963661180981

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

2.233 × 10⁹³(94-digit number)

22336565605864826585…75681073927322361959

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.233 × 10⁹³(94-digit number)

22336565605864826585…75681073927322361961

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

4.467 × 10⁹³(94-digit number)

44673131211729653170…51362147854644723919

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.467 × 10⁹³(94-digit number)

44673131211729653170…51362147854644723921

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

8.934 × 10⁹³(94-digit number)

89346262423459306341…02724295709289447839

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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