Block #469,595

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/1/2014, 8:29:31 AM · Difficulty 10.4272 · 6,345,453 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7caf7bf4d0f843763c59b9808cf4bab4dde97b857963e2c95a39e446f462075a

View on Chainz ↗

Height

#469,595

Difficulty

10.427234

Transactions

Size

27.36 KB

Version

Bits

0a6d5f3c

Nonce

122,026

Timestamp

4/1/2014, 8:29:31 AM

Confirmations

6,345,453

Mined by

AMVf7JrgD9LEuSS2R27DgQAdb3xd5AVR7C

Merkle Root

10e16a73ea480ad71223a91d07b2c26c3f27404b7cdd2e332cd82554a8002a3d

Transactions (2)

Coinbase2714a5d61b283e…3ba49adab177cf

1 in → 3 out9.4600 XPM165 B

AMVf7Jrg…xd5AVR7C ALzzzbUz…2Cb4jSDN AJno7LX2…vo4wdWtY

29c75e85f62177…d57a975522df0e

187 in → 2 out500.0100 XPM27.11 KB

AJjnK9uC…VreFquR4 ALoiJwNy…wNNZrP2Y

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.

9.887 × 10¹⁰¹(102-digit number)

98870226122962501868…07167372935494958079

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

9.887 × 10¹⁰¹(102-digit number)

98870226122962501868…07167372935494958079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.887 × 10¹⁰¹(102-digit number)

98870226122962501868…07167372935494958081

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

1.977 × 10¹⁰²(103-digit number)

19774045224592500373…14334745870989916159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.977 × 10¹⁰²(103-digit number)

19774045224592500373…14334745870989916161

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

3.954 × 10¹⁰²(103-digit number)

39548090449185000747…28669491741979832319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.954 × 10¹⁰²(103-digit number)

39548090449185000747…28669491741979832321

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

7.909 × 10¹⁰²(103-digit number)

79096180898370001494…57338983483959664639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.909 × 10¹⁰²(103-digit number)

79096180898370001494…57338983483959664641

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

1.581 × 10¹⁰³(104-digit number)

15819236179674000298…14677966967919329279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.581 × 10¹⁰³(104-digit number)

15819236179674000298…14677966967919329281

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 #469,595

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