Block #160,153

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 9/11/2013, 5:17:57 PM · Difficulty 9.8618 · 6,665,062 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f3d5ebc2cdbde99b64d845e48585a8f92100bec3304b349ce56e8beb92ce5c04

View on Chainz ↗

Height

#160,153

Difficulty

9.861807

Transactions

Size

1.71 KB

Version

Bits

09dc9f62

Nonce

9,008

Timestamp

9/11/2013, 5:17:57 PM

Confirmations

6,665,062

Mined by

⛏️ P2SHAWECiSsrgwEY2V8WNjkmsFYYfRbFpepHPG

Merkle Root

10a619132c04ca1e560df6658574f06a245b0caa0a440a671b91589051820ddc

Transactions (2)

Coinbase31400b7b61bac3…c13a00cdc13856

1 in → 1 out10.2900 XPM109 B

AWECiSsr…bFpepHPG

2a6b7583631299…067a7a4e9b03e9

10 in → 2 out500.0113 XPM1.52 KB

AQsbvQzs…RjpFZ4HH AUuj9v1F…ZtKeujSn

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.

1.223 × 10⁹¹(92-digit number)

12231614953779731920…19123186812293671149

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

1.223 × 10⁹¹(92-digit number)

12231614953779731920…19123186812293671149

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.223 × 10⁹¹(92-digit number)

12231614953779731920…19123186812293671151

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

2.446 × 10⁹¹(92-digit number)

24463229907559463840…38246373624587342299

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.446 × 10⁹¹(92-digit number)

24463229907559463840…38246373624587342301

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

4.892 × 10⁹¹(92-digit number)

48926459815118927681…76492747249174684599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.892 × 10⁹¹(92-digit number)

48926459815118927681…76492747249174684601

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

9.785 × 10⁹¹(92-digit number)

97852919630237855363…52985494498349369199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.785 × 10⁹¹(92-digit number)

97852919630237855363…52985494498349369201

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

1.957 × 10⁹²(93-digit number)

19570583926047571072…05970988996698738399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.957 × 10⁹²(93-digit number)

19570583926047571072…05970988996698738401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #160,153

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