Block #209,021

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/14/2013, 8:40:54 AM · Difficulty 9.9079 · 6,594,734 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0aa40ccacd0a721c155c3503e17be174f30da894e3d818ebf3ad5e3bf63030ee

View on Chainz ↗

Height

#209,021

Difficulty

9.907936

Transactions

Size

2.42 KB

Version

Bits

09e86e78

Nonce

49,400

Timestamp

10/14/2013, 8:40:54 AM

Confirmations

6,594,734

Mined by

⛏️ P2SHAbuU1HhSi58QcdzhwKqhpJiRG3JPwsJEbB

Merkle Root

2934e7ad3d1f55a8ce173886762e9d96a4a0c56b8b4a7dc35a82c944e96de525

Transactions (5)

Coinbase5f958eb8eed54d…3e9dbdef9980c2

1 in → 1 out10.2200 XPM110 B

AbuU1HhS…JPwsJEbB

9bc1c9e0ac8c46…78fddad39f0e41

10 in → 1 out101.9800 XPM1.16 KB

AbxSykSg…BX71twYi

3a4c913aa426af…3c7a9f1150801a

3 in → 2 out18.0997 XPM521 B

ASuoUi24…FwBoFbxd AcFxrT74…VBtVNNLW

3765d8fca0f4c8…e919d886b60a99

2 in → 1 out56.9637 XPM339 B

ATs2n3tY…z96nHXmV

c12c75681abb7f…a0157a1594eeb5

1 in → 2 out6.0417 XPM226 B

AWsge36A…wTk5iPiH Ac57QzjH…EYHHUHhF

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.

5.927 × 10¹⁰⁰(101-digit number)

59278962209846038968…96268842145598583599

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

5.927 × 10¹⁰⁰(101-digit number)

59278962209846038968…96268842145598583599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.927 × 10¹⁰⁰(101-digit number)

59278962209846038968…96268842145598583601

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

1.185 × 10¹⁰¹(102-digit number)

11855792441969207793…92537684291197167199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.185 × 10¹⁰¹(102-digit number)

11855792441969207793…92537684291197167201

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

2.371 × 10¹⁰¹(102-digit number)

23711584883938415587…85075368582394334399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.371 × 10¹⁰¹(102-digit number)

23711584883938415587…85075368582394334401

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

4.742 × 10¹⁰¹(102-digit number)

47423169767876831174…70150737164788668799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.742 × 10¹⁰¹(102-digit number)

47423169767876831174…70150737164788668801

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

9.484 × 10¹⁰¹(102-digit number)

94846339535753662348…40301474329577337599

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