Block #233,247

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/29/2013, 2:36:37 PM · Difficulty 9.9424 · 6,562,441 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

44eb049dc6a8ae715b1153ab6cc584d61457fd2a8416ae6486c36f87a03e0a00

View on Chainz ↗

Height

#233,247

Difficulty

9.942373

Transactions

Size

2.43 KB

Version

Bits

09f13f58

Nonce

7,403

Timestamp

10/29/2013, 2:36:37 PM

Confirmations

6,562,441

Mined by

⛏️ P2SHAMc3d2cpCs53w4rasCDD3ZAiFKDrSREBPX

Merkle Root

23c7f2a0fe9b8282cbe47eda5ff921351488ce34065af2fcf4cea59a7280c68e

Transactions (5)

Coinbaseb3aa927132e183…a303cba85b0431

1 in → 1 out10.1400 XPM109 B

AMc3d2cp…DrSREBPX

0cb7ee8e4ddc49…fdaff5a07c1dd7

3 in → 1 out30.3600 XPM384 B

AKN6pNCw…MeATKM2o

43074dde846393…bf518792de4280

5 in → 2 out30.8300 XPM718 B

AcSDRPvx…CZ2TbhTs AXjjCBZL…ntmdj2xe

42abe1e5b6a837…f67e939a2aa774

4 in → 2 out2.2140 XPM671 B

AaUFJEpX…pXH7JiXs AUsL6VH6…Du8VQEdZ

e15d1bc330acc1…931e1d54dd2bae

3 in → 2 out2.4237 XPM523 B

AaVFHFSq…bCnX1Bpw AQQrqgzL…4pnoUD8f

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.

1.617 × 10⁹⁰(91-digit number)

16172777781336771600…47375176257527509599

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

1.617 × 10⁹⁰(91-digit number)

16172777781336771600…47375176257527509599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.617 × 10⁹⁰(91-digit number)

16172777781336771600…47375176257527509601

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

3.234 × 10⁹⁰(91-digit number)

32345555562673543200…94750352515055019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.234 × 10⁹⁰(91-digit number)

32345555562673543200…94750352515055019201

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

6.469 × 10⁹⁰(91-digit number)

64691111125347086400…89500705030110038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.469 × 10⁹⁰(91-digit number)

64691111125347086400…89500705030110038401

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

1.293 × 10⁹¹(92-digit number)

12938222225069417280…79001410060220076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.293 × 10⁹¹(92-digit number)

12938222225069417280…79001410060220076801

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

2.587 × 10⁹¹(92-digit number)

25876444450138834560…58002820120440153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.587 × 10⁹¹(92-digit number)

25876444450138834560…58002820120440153601

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