Block #431,838

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/6/2014, 11:40:12 AM · Difficulty 10.3428 · 6,367,628 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

5555e7d3807b5fcc9f9ff4e083064e45e19095fae7d69f1833579c6f61a3f49a

View on Chainz ↗

Height

#431,838

Difficulty

10.342835

Transactions

Size

203 B

Version

Bits

0a57c40c

Nonce

26,434

Timestamp

3/6/2014, 11:40:12 AM

Confirmations

6,367,628

Mined by

⛏️ P2SHAVUSTGLfXSGYjUDuVVpW48qmaeSeYSsAGR

Merkle Root

beeccb2f60dee731e822d7a2e6e9eb483f342b096fc664f342ab168ee0bdcb42

Transactions (1)

Coinbasebeeccb2f60dee7…ab168ee0bdcb42

1 in → 1 out9.3300 XPM109 B

AVUSTGLf…SeYSsAGR

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.

4.950 × 10¹⁰³(104-digit number)

49504229340964194991…18685734350604159999

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

4.950 × 10¹⁰³(104-digit number)

49504229340964194991…18685734350604159999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.950 × 10¹⁰³(104-digit number)

49504229340964194991…18685734350604160001

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

9.900 × 10¹⁰³(104-digit number)

99008458681928389983…37371468701208319999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.900 × 10¹⁰³(104-digit number)

99008458681928389983…37371468701208320001

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

1.980 × 10¹⁰⁴(105-digit number)

19801691736385677996…74742937402416639999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.980 × 10¹⁰⁴(105-digit number)

19801691736385677996…74742937402416640001

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

3.960 × 10¹⁰⁴(105-digit number)

39603383472771355993…49485874804833279999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.960 × 10¹⁰⁴(105-digit number)

39603383472771355993…49485874804833280001

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

7.920 × 10¹⁰⁴(105-digit number)

79206766945542711986…98971749609666559999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.920 × 10¹⁰⁴(105-digit number)

79206766945542711986…98971749609666560001

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