Block #460,077

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/25/2014, 6:10:15 PM · Difficulty 10.4196 · 6,343,448 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3058eb3861b6b5ec8cc6df96eb0d027f1004d42d5626b7d5a03ba766a7f913d0

View on Chainz ↗

Height

#460,077

Difficulty

10.419595

Transactions

Size

656 B

Version

Bits

0a6b6a8f

Nonce

221,558

Timestamp

3/25/2014, 6:10:15 PM

Confirmations

6,343,448

Mined by

⛏️ P2SHAWP61hEiaZm3DZc3hxZMaedUsm1dnDFsZW

Merkle Root

96a597190d028c5def9ac9f7f8f55fefe2e17eddb641eec2f5b3d16a6da96b97

Transactions (3)

Coinbase81003dde072da3…15b07588528172

1 in → 1 out9.2200 XPM111 B

AWP61hEi…1dnDFsZW

507e8e64757520…5b9756ad5ab47e

1 in → 2 out4.0941 XPM227 B

AMDocE1E…LaRBVrTp AJ1g1qeX…mzdWHeoY

b820ce58088fe0…302f13e14de6b1

1 in → 2 out3.1464 XPM226 B

AXnL68UR…jsxeGUhN APUUrAaT…Rgdoa5HW

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.

8.750 × 10⁹⁸(99-digit number)

87506626189568913371…12101752865950879679

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

8.750 × 10⁹⁸(99-digit number)

87506626189568913371…12101752865950879679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.750 × 10⁹⁸(99-digit number)

87506626189568913371…12101752865950879681

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

1.750 × 10⁹⁹(100-digit number)

17501325237913782674…24203505731901759359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.750 × 10⁹⁹(100-digit number)

17501325237913782674…24203505731901759361

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

3.500 × 10⁹⁹(100-digit number)

35002650475827565348…48407011463803518719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.500 × 10⁹⁹(100-digit number)

35002650475827565348…48407011463803518721

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

7.000 × 10⁹⁹(100-digit number)

70005300951655130697…96814022927607037439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.000 × 10⁹⁹(100-digit number)

70005300951655130697…96814022927607037441

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

1.400 × 10¹⁰⁰(101-digit number)

14001060190331026139…93628045855214074879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.400 × 10¹⁰⁰(101-digit number)

14001060190331026139…93628045855214074881

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