Block #576,320

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/4/2014, 12:35:02 PM · Difficulty 10.9688 · 6,229,953 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c67721b693fb948468526ae3fca2cceb89d450ce082c7e7f9889a5e9419145fc

View on Chainz ↗

Height

#576,320

Difficulty

10.968789

Transactions

Size

878 B

Version

Bits

0af8028f

Nonce

105,886,828

Timestamp

6/4/2014, 12:35:02 PM

Confirmations

6,229,953

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

80d4984b92535e7660eff7be8d3bb5d93f9a357c70e012dcca4a37e787bef496

Transactions (2)

Coinbase2c92467d930e35…c914fe4739ff0c

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

5d0d3acbb33b20…bb1fd71b439b3f

4 in → 2 out3.1612 XPM670 B

AeKNrjNj…1NEq95Ta AY1FuBSV…jEZrVd1U

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.

3.636 × 10¹⁰⁰(101-digit number)

36362420525322311287…75992792578389032959

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

3.636 × 10¹⁰⁰(101-digit number)

36362420525322311287…75992792578389032959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.636 × 10¹⁰⁰(101-digit number)

36362420525322311287…75992792578389032961

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

7.272 × 10¹⁰⁰(101-digit number)

72724841050644622574…51985585156778065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.272 × 10¹⁰⁰(101-digit number)

72724841050644622574…51985585156778065921

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

1.454 × 10¹⁰¹(102-digit number)

14544968210128924514…03971170313556131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.454 × 10¹⁰¹(102-digit number)

14544968210128924514…03971170313556131841

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

2.908 × 10¹⁰¹(102-digit number)

29089936420257849029…07942340627112263679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.908 × 10¹⁰¹(102-digit number)

29089936420257849029…07942340627112263681

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

5.817 × 10¹⁰¹(102-digit number)

58179872840515698059…15884681254224527359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.817 × 10¹⁰¹(102-digit number)

58179872840515698059…15884681254224527361

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 #576,320

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