Block #633,736

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 7/15/2014, 12:37:49 AM · Difficulty 10.9640 · 6,174,240 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

93442e88e1608abde4f0ee71941ad23c80e4bf1a6f2a31aa4db6a16dff148cf1

View on Chainz ↗

Height

#633,736

Difficulty

10.964007

Transactions

Size

469 B

Version

Bits

0af6c922

Nonce

1,068,221,971

Timestamp

7/15/2014, 12:37:49 AM

Confirmations

6,174,240

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

6b55836fc321e800832dc783e8ef10836847218a66cfef0e6bf0e741edf9031d

Transactions (2)

Coinbasee04e24b34ea5f4…669e087a3423d0

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

61f8fe4d653e9f…171402b2ebc4a8

1 in → 3 out4.2593 XPM261 B

AJJqf2Po…tRLxW6P2 AeKNrjNj…1NEq95Ta AKc9Rmjx…Bir3N5mm

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.

2.184 × 10⁹⁹(100-digit number)

21845662691616272621…55440470470330502399

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

2.184 × 10⁹⁹(100-digit number)

21845662691616272621…55440470470330502399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.184 × 10⁹⁹(100-digit number)

21845662691616272621…55440470470330502401

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

4.369 × 10⁹⁹(100-digit number)

43691325383232545242…10880940940661004799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.369 × 10⁹⁹(100-digit number)

43691325383232545242…10880940940661004801

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

8.738 × 10⁹⁹(100-digit number)

87382650766465090485…21761881881322009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.738 × 10⁹⁹(100-digit number)

87382650766465090485…21761881881322009601

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

1.747 × 10¹⁰⁰(101-digit number)

17476530153293018097…43523763762644019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.747 × 10¹⁰⁰(101-digit number)

17476530153293018097…43523763762644019201

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

3.495 × 10¹⁰⁰(101-digit number)

34953060306586036194…87047527525288038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.495 × 10¹⁰⁰(101-digit number)

34953060306586036194…87047527525288038401

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

6.990 × 10¹⁰⁰(101-digit number)

69906120613172072388…74095055050576076799

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

Block #633,736

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