Block #184,631

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 9/28/2013, 7:13:18 PM · Difficulty 9.8601 · 6,629,603 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c9a2117a52e1bca942970050694ab45e5512e1fe8630a3152127d32a75ccb21e

View on Chainz ↗

Height

#184,631

Difficulty

9.860137

Transactions

Size

1.65 KB

Version

Bits

09dc31ef

Nonce

5,284

Timestamp

9/28/2013, 7:13:18 PM

Confirmations

6,629,603

Mined by

⛏️ P2SHAVJaZtXCr3NXSK79aMri9GXJU2gGZDZ3Yk

Merkle Root

2dd254741842377b6d32a8941ed4860ad0055ced4ef00ab24a1e979d8f16693c

Transactions (3)

Coinbase28308e0db8b1b8…99ccdf29a4a753

1 in → 1 out10.3000 XPM109 B

AVJaZtXC…gGZDZ3Yk

d21a31ce6ab38a…5d2edd7dd9dc0c

8 in → 2 out11.3840 XPM1.23 KB

AW5VXsNr…2xDYaWas AHyHEeYQ…XuELsExj

e05e2d2747ea12…2467eac4496673

1 in → 2 out4.0017 XPM226 B

AYeqvxBn…uDLc3xti AYjptRjJ…F1x2ZeUG

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.

7.454 × 10⁹⁴(95-digit number)

74542562472354036330…67159431624019956159

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

7.454 × 10⁹⁴(95-digit number)

74542562472354036330…67159431624019956159

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.454 × 10⁹⁴(95-digit number)

74542562472354036330…67159431624019956161

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

1.490 × 10⁹⁵(96-digit number)

14908512494470807266…34318863248039912319

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.490 × 10⁹⁵(96-digit number)

14908512494470807266…34318863248039912321

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

2.981 × 10⁹⁵(96-digit number)

29817024988941614532…68637726496079824639

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.981 × 10⁹⁵(96-digit number)

29817024988941614532…68637726496079824641

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

5.963 × 10⁹⁵(96-digit number)

59634049977883229064…37275452992159649279

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.963 × 10⁹⁵(96-digit number)

59634049977883229064…37275452992159649281

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

1.192 × 10⁹⁶(97-digit number)

11926809995576645812…74550905984319298559

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 #184,631

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