Block #19,203

TWNLength 7★☆☆☆☆

Bi-Twin Chain · Discovered 7/12/2013, 8:09:41 AM · Difficulty 7.9185 · 6,776,277 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

742cbbaf65cc6efed052fab4dbeed2d054ad422ab6ee4d1841f37a89822358a0

View on Chainz ↗

Height

#19,203

Difficulty

7.918550

Transactions

Size

200 B

Version

Bits

07eb2617

Nonce

187

Timestamp

7/12/2013, 8:09:41 AM

Confirmations

6,776,277

Mined by

⛏️ P2SHAexogkVA6p3nMVBvGxJuwyy43rbGe9WHvw

Merkle Root

1e02312aed6bce14077b4514bbca5eee5bc0cbb7169d465ed7d729d799e93bc6

Transactions (1)

Coinbase1e02312aed6bce…d729d799e93bc6

1 in → 1 out15.9300 XPM108 B

AexogkVA…bGe9WHvw

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.

1.464 × 10¹⁰⁰(101-digit number)

14646220472745665353…37851353850638331499

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

1.464 × 10¹⁰⁰(101-digit number)

14646220472745665353…37851353850638331499

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.464 × 10¹⁰⁰(101-digit number)

14646220472745665353…37851353850638331501

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

2.929 × 10¹⁰⁰(101-digit number)

29292440945491330706…75702707701276662999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.929 × 10¹⁰⁰(101-digit number)

29292440945491330706…75702707701276663001

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

5.858 × 10¹⁰⁰(101-digit number)

58584881890982661412…51405415402553325999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.858 × 10¹⁰⁰(101-digit number)

58584881890982661412…51405415402553326001

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

1.171 × 10¹⁰¹(102-digit number)

11716976378196532282…02810830805106651999

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