Block #48,960

TWNLength 8★☆☆☆☆

Bi-Twin Chain · Discovered 7/15/2013, 5:54:31 PM · Difficulty 8.8558 · 6,778,115 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

1fa867b59c10655ba225b11f919c312a532006e1b2fd982f4949f0f1adc6810e

View on Chainz ↗

Height

#48,960

Difficulty

8.855759

Transactions

Size

1.65 KB

Version

Bits

08db1304

Nonce

1,835

Timestamp

7/15/2013, 5:54:31 PM

Confirmations

6,778,115

Mined by

⛏️ P2SHAGAB5evB5jLKLQ3tAW3p1vLfxdknAkpFjt

Merkle Root

612e67b1edb8c1895e8b4f70f0cc2aca984737f23e7183eb74d4b50a9a1ea55c

Transactions (3)

Coinbasefb507ab68eba6a…70f66a7d4f8866

1 in → 1 out12.7600 XPM110 B

AGAB5evB…knAkpFjt

2050c972eff329…1d7b161c0bd39b

11 in → 1 out129.9600 XPM1.30 KB

ARsrDwcp…Fv5SKr8Y

c9a676613b6d96…e31aba458ce128

1 in → 1 out12.9800 XPM158 B

AHkEa2Pq…tUzrKxgF

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.

2.861 × 10⁹⁶(97-digit number)

28610149391473764453…95149845218811755099

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

2.861 × 10⁹⁶(97-digit number)

28610149391473764453…95149845218811755099

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.861 × 10⁹⁶(97-digit number)

28610149391473764453…95149845218811755101

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

5.722 × 10⁹⁶(97-digit number)

57220298782947528907…90299690437623510199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.722 × 10⁹⁶(97-digit number)

57220298782947528907…90299690437623510201

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

1.144 × 10⁹⁷(98-digit number)

11444059756589505781…80599380875247020399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.144 × 10⁹⁷(98-digit number)

11444059756589505781…80599380875247020401

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

2.288 × 10⁹⁷(98-digit number)

22888119513179011563…61198761750494040799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.288 × 10⁹⁷(98-digit number)

22888119513179011563…61198761750494040801

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

Block #48,960

Cookie Preferences