Block #75,614

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/21/2013, 5:38:17 PM · Difficulty 9.0229 · 6,741,515 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

19225ccfe8096d4aa52bc5fcc7240b619969670d7c43bff7213199a69dc07c2c

View on Chainz ↗

Height

#75,614

Difficulty

9.022933

Transactions

Size

734 B

Version

Bits

0905def2

Nonce

770

Timestamp

7/21/2013, 5:38:17 PM

Confirmations

6,741,515

Mined by

⛏️ P2SHAGfT7GUdSmAc84Vgz2FDcG8rMMvLtmbjrx

Merkle Root

eb07993a2048fae13d12ccec4b44a352ab5c5bf96e3da683a909b7b4ca398472

Transactions (3)

Coinbase37da135cc33f0e…81de2d34a6b64c

1 in → 1 out12.2900 XPM110 B

AGfT7GUd…vLtmbjrx

f62af9f47106a1…ff2d01a2e947f8

2 in → 2 out129.1900 XPM372 B

AHpBMX8u…iwonAzfW AWgLSjbC…8aJ5fgEn

4448aa0ff6cf47…80439108c38e8a

1 in → 1 out12.3300 XPM158 B

ANBXgfaf…ZXqNYSdt

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.

4.086 × 10¹⁰³(104-digit number)

40869303862589817653…53081934430224190899

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

4.086 × 10¹⁰³(104-digit number)

40869303862589817653…53081934430224190899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.086 × 10¹⁰³(104-digit number)

40869303862589817653…53081934430224190901

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

8.173 × 10¹⁰³(104-digit number)

81738607725179635306…06163868860448381799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.173 × 10¹⁰³(104-digit number)

81738607725179635306…06163868860448381801

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

1.634 × 10¹⁰⁴(105-digit number)

16347721545035927061…12327737720896763599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.634 × 10¹⁰⁴(105-digit number)

16347721545035927061…12327737720896763601

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

3.269 × 10¹⁰⁴(105-digit number)

32695443090071854122…24655475441793527199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.269 × 10¹⁰⁴(105-digit number)

32695443090071854122…24655475441793527201

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

6.539 × 10¹⁰⁴(105-digit number)

65390886180143708245…49310950883587054399

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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 9

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 #75,614

Cookie Preferences