Block #234,668

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/30/2013, 11:27:59 AM · Difficulty 9.9444 · 6,556,815 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fb56ca63893196ecae6850410015488c9ee44cfa5309d5ac58f98ad8d9332336

View on Chainz ↗

Height

#234,668

Difficulty

9.944358

Transactions

Size

425 B

Version

Bits

09f1c177

Nonce

511,455

Timestamp

10/30/2013, 11:27:59 AM

Confirmations

6,556,815

Merkle Root

aadeccd390b23d3dc75e4a14c91d0a7575e0f6a8801191c60f3de644bce9d4a0

Transactions (2)

Coinbase9f3cf35dca16d3…3abbcf339fd219

1 in → 1 out10.1100 XPM109 B

ATnbm6QG…aaoEpmBU

bebd1f6d469446…06f754ae960c15

1 in → 2 out4.9427 XPM227 B

AGYCd86d…m2q4rrUW ASnSjgQg…fewAaNPL

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.

3.563 × 10⁹²(93-digit number)

35634638276324373655…67059015086109688799

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

3.563 × 10⁹²(93-digit number)

35634638276324373655…67059015086109688799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.563 × 10⁹²(93-digit number)

35634638276324373655…67059015086109688801

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

7.126 × 10⁹²(93-digit number)

71269276552648747310…34118030172219377599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.126 × 10⁹²(93-digit number)

71269276552648747310…34118030172219377601

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

1.425 × 10⁹³(94-digit number)

14253855310529749462…68236060344438755199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.425 × 10⁹³(94-digit number)

14253855310529749462…68236060344438755201

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

2.850 × 10⁹³(94-digit number)

28507710621059498924…36472120688877510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.850 × 10⁹³(94-digit number)

28507710621059498924…36472120688877510401

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

5.701 × 10⁹³(94-digit number)

57015421242118997848…72944241377755020799

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