Block #185,584

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/29/2013, 9:55:50 AM · Difficulty 9.8623 · 6,629,522 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

32b663894d01395a3a07a308f7c9ff1e2e3e1df28ded69770f3823625cf7504e

View on Chainz ↗

Height

#185,584

Difficulty

9.862284

Transactions

Size

798 B

Version

Bits

09dcbe9f

Nonce

45,899

Timestamp

9/29/2013, 9:55:50 AM

Confirmations

6,629,522

Mined by

⛏️ P2SHARqRRxfREjy9RTKuN9vtpoVYde4VntLx4S

Merkle Root

84bd33a644ddbac0868d4c7dffe65264a9bd93b50438c5e7a307f07657a0eb6d

Transactions (3)

Coinbasea2c496aaba4ae7…922792e995af77

1 in → 1 out10.2900 XPM109 B

ARqRRxfR…4VntLx4S

f5b1a435d67ecf…201528f89302a9

2 in → 2 out16.2959 XPM374 B

ALpthvGg…D1g5z4CT ASa4KWnS…CseDqa2W

9c4371696d7e6f…5b7f6c6b1f462b

1 in → 2 out6.1648 XPM227 B

AYBXoSUq…MR3uYbc4 AUfBNY3y…Mm2UYiNj

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.

1.429 × 10⁹⁰(91-digit number)

14291665696155251614…40445344965197518399

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

1.429 × 10⁹⁰(91-digit number)

14291665696155251614…40445344965197518399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.429 × 10⁹⁰(91-digit number)

14291665696155251614…40445344965197518401

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

2.858 × 10⁹⁰(91-digit number)

28583331392310503229…80890689930395036799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.858 × 10⁹⁰(91-digit number)

28583331392310503229…80890689930395036801

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

5.716 × 10⁹⁰(91-digit number)

57166662784621006458…61781379860790073599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.716 × 10⁹⁰(91-digit number)

57166662784621006458…61781379860790073601

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

1.143 × 10⁹¹(92-digit number)

11433332556924201291…23562759721580147199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.143 × 10⁹¹(92-digit number)

11433332556924201291…23562759721580147201

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

2.286 × 10⁹¹(92-digit number)

22866665113848402583…47125519443160294399

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 #185,584

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