Block #427,059

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/3/2014, 3:13:58 AM · Difficulty 10.3461 · 6,375,708 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3da2ff6ed149e1347925ac8275f1e8ceea4d348f471ba9a1c86a386bfcf48809

View on Chainz ↗

Height

#427,059

Difficulty

10.346111

Transactions

Size

884 B

Version

Bits

0a589ac0

Nonce

62,412

Timestamp

3/3/2014, 3:13:58 AM

Confirmations

6,375,708

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

bd6e76e6fac6afd7155997ca35013603a4d1d6dea7641dfb71b2a853a1734367

Transactions (4)

Coinbase01cd91f6520382…b89f1e36f37b62

1 in → 1 out9.3600 XPM110 B

AeKNrjNj…1NEq95Ta

994ee34837fca1…8da14d994a567e

1 in → 2 out6.1617 XPM227 B

Adf7bYFv…xUwcaCNF ARsgnnD3…NGfS5PVM

d01c44f8b55319…daa21825699d23

1 in → 2 out5.1436 XPM226 B

AL6CNP6y…5kFfo8Ht AZ4vQEb5…k7Li1iHB

da3c01515008b9…310e6f183971b5

1 in → 2 out2.0910 XPM227 B

AVeTozdt…yWaeexTx AXhWtbPt…5LyuGMVA

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.

1.635 × 10¹⁰⁴(105-digit number)

16353268974399681962…70987754929357004799

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

1.635 × 10¹⁰⁴(105-digit number)

16353268974399681962…70987754929357004799

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.635 × 10¹⁰⁴(105-digit number)

16353268974399681962…70987754929357004801

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

3.270 × 10¹⁰⁴(105-digit number)

32706537948799363924…41975509858714009599

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.270 × 10¹⁰⁴(105-digit number)

32706537948799363924…41975509858714009601

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

6.541 × 10¹⁰⁴(105-digit number)

65413075897598727849…83951019717428019199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.541 × 10¹⁰⁴(105-digit number)

65413075897598727849…83951019717428019201

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

1.308 × 10¹⁰⁵(106-digit number)

13082615179519745569…67902039434856038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.308 × 10¹⁰⁵(106-digit number)

13082615179519745569…67902039434856038401

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

2.616 × 10¹⁰⁵(106-digit number)

26165230359039491139…35804078869712076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.616 × 10¹⁰⁵(106-digit number)

26165230359039491139…35804078869712076801

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