Block #567,077

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/29/2014, 11:45:54 AM · Difficulty 10.9649 · 6,239,030 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

16ce3c96b0731a7b25a27b3046d33447724c25fe16cb2aacb6a1f70978ac3241

View on Chainz ↗

Height

#567,077

Difficulty

10.964861

Transactions

Size

843 B

Version

Bits

0af7011a

Nonce

230,788,272

Timestamp

5/29/2014, 11:45:54 AM

Confirmations

6,239,030

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

58b93e6fbbb95c6752bc2bf832dd682d852142d9ca4d3cabc507de2d50570862

Transactions (3)

Coinbase6d53018823543a…7e988afe49ed60

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

0d2936468326d3…b75a8cc234ae29

2 in → 4 out9.5734 XPM408 B

AK6P7xdW…xLXseJWb AL48EMca…MMV6JRSc ANGAxNk6…Bb4uN2Ub AeKNrjNj…1NEq95Ta

904831b446225b…174ce2f4412524

1 in → 2 out3.1527 XPM226 B

AUvh5QcY…dRMJwJ84 AULkviz4…6ZwMzqc9

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.

4.972 × 10¹⁰⁰(101-digit number)

49727970150986719270…71090013932292177919

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

4.972 × 10¹⁰⁰(101-digit number)

49727970150986719270…71090013932292177919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.972 × 10¹⁰⁰(101-digit number)

49727970150986719270…71090013932292177921

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

9.945 × 10¹⁰⁰(101-digit number)

99455940301973438540…42180027864584355839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.945 × 10¹⁰⁰(101-digit number)

99455940301973438540…42180027864584355841

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

1.989 × 10¹⁰¹(102-digit number)

19891188060394687708…84360055729168711679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.989 × 10¹⁰¹(102-digit number)

19891188060394687708…84360055729168711681

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

3.978 × 10¹⁰¹(102-digit number)

39782376120789375416…68720111458337423359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.978 × 10¹⁰¹(102-digit number)

39782376120789375416…68720111458337423361

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

7.956 × 10¹⁰¹(102-digit number)

79564752241578750832…37440222916674846719

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.956 × 10¹⁰¹(102-digit number)

79564752241578750832…37440222916674846721

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.591 × 10¹⁰²(103-digit number)

15912950448315750166…74880445833349693439

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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