Block #48,923

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 5:41:00 PM · Difficulty 8.8551 · 6,745,954 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2f3425a89e7d18e40ba92dcac2a29aecf40a7129f3061f164106cd5271358dfa

View on Chainz ↗

Height

#48,923

Difficulty

8.855106

Transactions

Size

1.21 KB

Version

Bits

08dae83d

Nonce

510

Timestamp

7/15/2013, 5:41:00 PM

Confirmations

6,745,954

Mined by

⛏️ P2SHAa9FhQpaAVqbia17fG1PH6skGt3pXbJcAv

Merkle Root

95f1d3850da7fe7330e8afee40c52aaeeee13af369a10a61b882c14411030271

Transactions (5)

Coinbaseb60c0cd2628864…ebb7625c001ddc

1 in → 1 out12.7800 XPM110 B

Aa9FhQpa…3pXbJcAv

9fd00aebb2543c…84ce4b8ab89ed6

3 in → 1 out26.9900 XPM420 B

AYXPRHd7…gbjLt25D

467758c3bed934…abe1187b21dc1e

1 in → 1 out12.9900 XPM158 B

AHkEa2Pq…tUzrKxgF

98fa4d3d7d22af…96a3257774d6c6

1 in → 2 out659.9900 XPM227 B

AaEohaBT…bCFyFubV AecWEyiC…Txv2qbrw

d60c5cdac4bba1…498a4c031d81c2

1 in → 2 out0.3500 XPM226 B

AZnwAHSy…FqPt4EMT ALMDqcqh…BUVrWgRA

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.

5.691 × 10¹⁰³(104-digit number)

56919718250282725677…15638959848993987959

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

5.691 × 10¹⁰³(104-digit number)

56919718250282725677…15638959848993987959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.691 × 10¹⁰³(104-digit number)

56919718250282725677…15638959848993987961

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

1.138 × 10¹⁰⁴(105-digit number)

11383943650056545135…31277919697987975919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.138 × 10¹⁰⁴(105-digit number)

11383943650056545135…31277919697987975921

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

2.276 × 10¹⁰⁴(105-digit number)

22767887300113090271…62555839395975951839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.276 × 10¹⁰⁴(105-digit number)

22767887300113090271…62555839395975951841

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

4.553 × 10¹⁰⁴(105-digit number)

45535774600226180542…25111678791951903679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.553 × 10¹⁰⁴(105-digit number)

45535774600226180542…25111678791951903681

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 8 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

CommonChain length 8

Found in most blocks. The baseline for Primecoin's proof-of-work.

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