Block #491,017

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/14/2014, 5:50:12 AM · Difficulty 10.6802 · 6,318,107 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

726796b5f720f4131328df74bc16c3eac20ff64f768e36fb067bc09c7f018064

View on Chainz ↗

Height

#491,017

Difficulty

10.680223

Transactions

Size

1.23 KB

Version

Bits

0aae2320

Nonce

2,837

Timestamp

4/14/2014, 5:50:12 AM

Confirmations

6,318,107

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

79111097fad003c81ee7f287ddf84cfe320ec87b281aed66639ac14154ddc81f

Transactions (5)

Coinbase2f6126480ccf6f…8a21c44bc32a28

1 in → 1 out8.7900 XPM116 B

AbwWkWZt…kawDhufa

cafc4337d9a252…2faea900483bb5

1 in → 2 out8.8000 XPM225 B

Ad68YKwp…YD5R7L76 AKTVLd3e…rRVkaemb

6bef7350e5213b…e2883f2ebbb82f

1 in → 2 out8.8000 XPM226 B

AJggGBSF…ioWg4H8E AJe4n8vD…FBJCBcVz

44d2f47d048ec6…724c4f7508456f

1 in → 2 out5.7566 XPM227 B

ATNFVyQ2…LVuA6grF AdeCnJdd…nP6ys3Vg

062f7982ee8202…47c6c136e32d42

2 in → 2 out1.0403 XPM376 B

AVWikeRB…3VmEkuMw AVR9s4fa…AW7C55ZT

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.

1.808 × 10¹⁰¹(102-digit number)

18085421965938208948…51001167326412927999

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

1.808 × 10¹⁰¹(102-digit number)

18085421965938208948…51001167326412927999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.808 × 10¹⁰¹(102-digit number)

18085421965938208948…51001167326412928001

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

3.617 × 10¹⁰¹(102-digit number)

36170843931876417897…02002334652825855999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.617 × 10¹⁰¹(102-digit number)

36170843931876417897…02002334652825856001

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

7.234 × 10¹⁰¹(102-digit number)

72341687863752835794…04004669305651711999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.234 × 10¹⁰¹(102-digit number)

72341687863752835794…04004669305651712001

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

1.446 × 10¹⁰²(103-digit number)

14468337572750567158…08009338611303423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.446 × 10¹⁰²(103-digit number)

14468337572750567158…08009338611303424001

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

2.893 × 10¹⁰²(103-digit number)

28936675145501134317…16018677222606847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.893 × 10¹⁰²(103-digit number)

28936675145501134317…16018677222606848001

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 #491,017

Cookie Preferences