Block #53,682

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/16/2013, 4:31:59 PM · Difficulty 8.9261 · 6,763,091 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7b36722483b5d55cd7302e48a670af271bfc491d420efc1977c26d4277931dea

View on Chainz ↗

Height

#53,682

Difficulty

8.926113

Transactions

Size

1.48 KB

Version

Bits

08ed15bb

Nonce

Timestamp

7/16/2013, 4:31:59 PM

Confirmations

6,763,091

Mined by

⛏️ P2SHAaGiSz2C6cgdYwdmDcB5bEJVLEyRcgbjBV

Merkle Root

f160ef618ef23335d098451d8cafe3c7017dda3455130acc4f4afb213081e0ce

Transactions (3)

Coinbasecdd8f84baff698…6bd356164f0546

1 in → 1 out12.5500 XPM110 B

AaGiSz2C…yRcgbjBV

2a1b51474a5fea…d7a4258a88d25e

4 in → 1 out51.3400 XPM502 B

AWZPS4WA…7LQazeJT

93e998a2673cbf…bf991ad225c913

5 in → 2 out59.9164 XPM817 B

AK3x8dvE…nYbmJccD AYq5yhXu…xUKqjVfe

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.

1.549 × 10⁹³(94-digit number)

15498272531160450006…66962597734974522579

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

1.549 × 10⁹³(94-digit number)

15498272531160450006…66962597734974522579

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.549 × 10⁹³(94-digit number)

15498272531160450006…66962597734974522581

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

3.099 × 10⁹³(94-digit number)

30996545062320900013…33925195469949045159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.099 × 10⁹³(94-digit number)

30996545062320900013…33925195469949045161

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

6.199 × 10⁹³(94-digit number)

61993090124641800026…67850390939898090319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.199 × 10⁹³(94-digit number)

61993090124641800026…67850390939898090321

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

1.239 × 10⁹⁴(95-digit number)

12398618024928360005…35700781879796180639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.239 × 10⁹⁴(95-digit number)

12398618024928360005…35700781879796180641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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 8

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 #53,682

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