Block #24,486

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 11:10:55 PM · Difficulty 7.9660 · 6,767,836 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8e3f7ec07fd06abc9dc5e31f6b1d1031cfacf52c313929e8b2c43ad23466ffd0

View on Chainz ↗

Height

#24,486

Difficulty

7.965963

Transactions

Size

8.93 KB

Version

Bits

07f74952

Nonce

Timestamp

7/12/2013, 11:10:55 PM

Confirmations

6,767,836

Merkle Root

e7bd2e214e3469234e9ca49e35dba2380be90dfeef4436c3e69f2e66b2b3d0fc

Transactions (2)

Coinbasee9a2976f60faae…e110c09b56a33d

1 in → 1 out15.8300 XPM108 B

AGemJXng…w1K3MEut

87f86610efcdc8…c605a7c49ec605

78 in → 1 out1396.7000 XPM8.73 KB

AJs8PqS2…wyt2WdLg

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.

2.683 × 10¹⁰³(104-digit number)

26837220419788141689…40586780088540285289

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

2.683 × 10¹⁰³(104-digit number)

26837220419788141689…40586780088540285289

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.683 × 10¹⁰³(104-digit number)

26837220419788141689…40586780088540285291

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

5.367 × 10¹⁰³(104-digit number)

53674440839576283378…81173560177080570579

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.367 × 10¹⁰³(104-digit number)

53674440839576283378…81173560177080570581

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

1.073 × 10¹⁰⁴(105-digit number)

10734888167915256675…62347120354161141159

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.073 × 10¹⁰⁴(105-digit number)

10734888167915256675…62347120354161141161

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

2.146 × 10¹⁰⁴(105-digit number)

21469776335830513351…24694240708322282319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 7 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 7

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