Block #667,003

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/7/2014, 9:54:06 AM · Difficulty 10.9619 · 6,138,685 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4035224f6b174db97cc8e84815cfba863b3c9f335881a6821c710c516c7fda12

View on Chainz ↗

Height

#667,003

Difficulty

10.961899

Transactions

Size

1.77 KB

Version

Bits

0af63f0b

Nonce

375,745,215

Timestamp

8/7/2014, 9:54:06 AM

Confirmations

6,138,685

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e7e2e84d06cb1c06274af5ad3b43d7d8bf717c8cde2567a3b7d6583240c9f76b

Transactions (3)

Coinbasecf3c685758f4fe…c7b2d9237f34e3

1 in → 1 out8.3400 XPM116 B

ANSXnLY2…Sd25TjkD

50c481705bfd27…4844e950d739fd

1 in → 2 out8.3000 XPM192 B

APxbhVhR…sLattjxW AWbYt63i…H2mAW2Wz

37dccd3e002975…697d98d598073b

9 in → 2 out7.6191 XPM1.38 KB

AMcZysWs…soiCCJ5Q AUoMMSiV…fVpRqJ1d

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.

1.261 × 10⁹⁵(96-digit number)

12615054195754686580…12385807756367259399

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

1.261 × 10⁹⁵(96-digit number)

12615054195754686580…12385807756367259399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.261 × 10⁹⁵(96-digit number)

12615054195754686580…12385807756367259401

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

2.523 × 10⁹⁵(96-digit number)

25230108391509373160…24771615512734518799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.523 × 10⁹⁵(96-digit number)

25230108391509373160…24771615512734518801

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

5.046 × 10⁹⁵(96-digit number)

50460216783018746321…49543231025469037599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.046 × 10⁹⁵(96-digit number)

50460216783018746321…49543231025469037601

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

1.009 × 10⁹⁶(97-digit number)

10092043356603749264…99086462050938075199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.009 × 10⁹⁶(97-digit number)

10092043356603749264…99086462050938075201

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

2.018 × 10⁹⁶(97-digit number)

20184086713207498528…98172924101876150399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.018 × 10⁹⁶(97-digit number)

20184086713207498528…98172924101876150401

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

4.036 × 10⁹⁶(97-digit number)

40368173426414997056…96345848203752300799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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