Block #466,792

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/30/2014, 9:34:03 AM · Difficulty 10.4270 · 6,347,221 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

4bd02b7a608cf40de2e7a2c3c291eaf296b3380f961bf76001c14507e544c15b

View on Chainz ↗

Height

#466,792

Difficulty

10.426954

Transactions

Size

428 B

Version

Bits

0a6d4cd9

Nonce

131,971

Timestamp

3/30/2014, 9:34:03 AM

Confirmations

6,347,221

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

b2bb74bf08f40db74ff727cf4cfe6f01215417dddf94c8a6c4b89daa9fd1ab3e

Transactions (2)

Coinbase721a5feef2c907…7414f2543d6638

1 in → 1 out9.1900 XPM110 B

AeKNrjNj…1NEq95Ta

9e6a0f35de6c91…a74eeea0dab0aa

1 in → 2 out3.3073 XPM226 B

AGUJNGUR…MVoKjwHq AGRC2bmC…LnFawpob

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.

9.988 × 10⁹⁸(99-digit number)

99883995734807079148…31852969703208642559

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

9.988 × 10⁹⁸(99-digit number)

99883995734807079148…31852969703208642559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.988 × 10⁹⁸(99-digit number)

99883995734807079148…31852969703208642561

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

1.997 × 10⁹⁹(100-digit number)

19976799146961415829…63705939406417285119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.997 × 10⁹⁹(100-digit number)

19976799146961415829…63705939406417285121

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

3.995 × 10⁹⁹(100-digit number)

39953598293922831659…27411878812834570239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.995 × 10⁹⁹(100-digit number)

39953598293922831659…27411878812834570241

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

7.990 × 10⁹⁹(100-digit number)

79907196587845663319…54823757625669140479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.990 × 10⁹⁹(100-digit number)

79907196587845663319…54823757625669140481

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

1.598 × 10¹⁰⁰(101-digit number)

15981439317569132663…09647515251338280959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.598 × 10¹⁰⁰(101-digit number)

15981439317569132663…09647515251338280961

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 #466,792

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