Block #241,950

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 11/3/2013, 12:05:38 PM · Difficulty 9.9588 · 6,591,239 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe63a9c0c066cadc898ebf16b1bc0ae06e584df5ee1de192a447691e935ab2ce

View on Chainz ↗

Height

#241,950

Difficulty

9.958808

Transactions

Size

830 B

Version

Bits

09f57470

Nonce

15,756

Timestamp

11/3/2013, 12:05:38 PM

Confirmations

6,591,239

Mined by

⛏️ P2SHAZDUEbdSvp8cw8AAZ1fERZUqSYRYKMRZET

Merkle Root

7b791b8bb3c066b8b6cd4e7bffc7a3ea52ae8978f0a0331b16d35df01d4a840c

Transactions (3)

Coinbase0fe6f663c9874f…0e8869266cb13b

1 in → 2 out10.0900 XPM136 B

AZDUEbdS…RYKMRZET ALfEGCwh…VawujfMm

43f4f1f5ecd19e…4d410ccb561b5b

1 in → 2 out5.0599 XPM227 B

AKTpFREV…j5nFmAna AaVFHFSq…bCnX1Bpw

fd9d8698d11dce…bfce3054fdb028

2 in → 2 out6.0250 XPM374 B

AV5DuG9A…2oo2dY4m ARC34c2B…XiBBrx4X

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.

3.998 × 10¹⁰¹(102-digit number)

39989496038448320469…68696508734341964799

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

3.998 × 10¹⁰¹(102-digit number)

39989496038448320469…68696508734341964799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.998 × 10¹⁰¹(102-digit number)

39989496038448320469…68696508734341964801

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

7.997 × 10¹⁰¹(102-digit number)

79978992076896640938…37393017468683929599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.997 × 10¹⁰¹(102-digit number)

79978992076896640938…37393017468683929601

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

1.599 × 10¹⁰²(103-digit number)

15995798415379328187…74786034937367859199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.599 × 10¹⁰²(103-digit number)

15995798415379328187…74786034937367859201

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

3.199 × 10¹⁰²(103-digit number)

31991596830758656375…49572069874735718399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.199 × 10¹⁰²(103-digit number)

31991596830758656375…49572069874735718401

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

6.398 × 10¹⁰²(103-digit number)

63983193661517312750…99144139749471436799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.398 × 10¹⁰²(103-digit number)

63983193661517312750…99144139749471436801

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 #241,950

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