Block #507,206

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/23/2014, 2:14:17 PM · Difficulty 10.8158 · 6,319,903 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

135b954362b80c698601b554872383eec8adc1fe5ddff49eac101c2c259c4fcb

View on Chainz ↗

Height

#507,206

Difficulty

10.815792

Transactions

Size

960 B

Version

Bits

0ad0d7c1

Nonce

196,443

Timestamp

4/23/2014, 2:14:17 PM

Confirmations

6,319,903

Mined by

⛏️ FAREQGaCCeRHuaNkf53p3iT4PbrV47D9Shh

Merkle Root

53b3690653074e087be9951008d46b62b2a27501c419b3238b8789af00674e27

Transactions (2)

Coinbase73a9cf18506980…ca7e8c9bdc8f6c

1 in → 18 out8.5400 XPM675 B

AREQGaCC…V47D9Shh AGz9gyZW…bo8NYQpw AUFKXvnz…342ApNcm AXCpMYgL…1r94ZQDa AbPcCMg4…719q6mAX

3e226c68efdb49…a0f8014ae03389

1 in → 1 out0.3320 XPM192 B

AGXFqSyj…FxquNuxH

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.

8.768 × 10¹⁰⁰(101-digit number)

87682047822021946174…51622811300028097279

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

8.768 × 10¹⁰⁰(101-digit number)

87682047822021946174…51622811300028097279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.768 × 10¹⁰⁰(101-digit number)

87682047822021946174…51622811300028097281

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

1.753 × 10¹⁰¹(102-digit number)

17536409564404389234…03245622600056194559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.753 × 10¹⁰¹(102-digit number)

17536409564404389234…03245622600056194561

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

3.507 × 10¹⁰¹(102-digit number)

35072819128808778469…06491245200112389119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.507 × 10¹⁰¹(102-digit number)

35072819128808778469…06491245200112389121

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

7.014 × 10¹⁰¹(102-digit number)

70145638257617556939…12982490400224778239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.014 × 10¹⁰¹(102-digit number)

70145638257617556939…12982490400224778241

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

1.402 × 10¹⁰²(103-digit number)

14029127651523511387…25964980800449556479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.402 × 10¹⁰²(103-digit number)

14029127651523511387…25964980800449556481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #507,206

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