Block #2,238,224

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 8/5/2017, 3:35:32 PM · Difficulty 10.9461 · 4,604,347 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7e1ae26a4c5abb0f71032ae11d802c57beb7a78e09adb853c3f66df575fc7c62

View on Chainz ↗

Height

#2,238,224

Difficulty

10.946134

Transactions

Size

425 B

Version

Bits

0af235d3

Nonce

418,963,027

Timestamp

8/5/2017, 3:35:32 PM

Confirmations

4,604,347

Mined by

⛏️ P2SHAUzyELTw9TA2XMX3ENZj4iUobRfM1B4YsQ

Merkle Root

66fa3166c9b0e83fccbf45bdd06d11cad3c450015a93d0b167c284f2a3be0aca

Transactions (2)

Coinbase209153ca2a067b…ffc891cdd65ddc

1 in → 1 out8.3400 XPM110 B

AUzyELTw…fM1B4YsQ

55626f02584f5a…f18218fc479412

1 in → 2 out1979.9900 XPM225 B

ANKBTLg6…nGXvR6LD AbqXRqrX…93pFH86f

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.

2.697 × 10⁹⁵(96-digit number)

26972423824714653807…63943576403257000959

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

2.697 × 10⁹⁵(96-digit number)

26972423824714653807…63943576403257000959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.697 × 10⁹⁵(96-digit number)

26972423824714653807…63943576403257000961

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

5.394 × 10⁹⁵(96-digit number)

53944847649429307614…27887152806514001919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.394 × 10⁹⁵(96-digit number)

53944847649429307614…27887152806514001921

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

1.078 × 10⁹⁶(97-digit number)

10788969529885861522…55774305613028003839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.078 × 10⁹⁶(97-digit number)

10788969529885861522…55774305613028003841

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

2.157 × 10⁹⁶(97-digit number)

21577939059771723045…11548611226056007679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.157 × 10⁹⁶(97-digit number)

21577939059771723045…11548611226056007681

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

4.315 × 10⁹⁶(97-digit number)

43155878119543446091…23097222452112015359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.315 × 10⁹⁶(97-digit number)

43155878119543446091…23097222452112015361

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

8.631 × 10⁹⁶(97-digit number)

86311756239086892183…46194444904224030719

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 #2,238,224

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