Block #571,414

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/1/2014, 11:22:43 AM · Difficulty 10.9653 · 6,234,502 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d47556aa66827d6327be71f5ab112ef2b3bf0a101568fbab7d3185e6aa18d4bc

View on Chainz ↗

Height

#571,414

Difficulty

10.965283

Transactions

Size

883 B

Version

Bits

0af71ccd

Nonce

36,844,905

Timestamp

6/1/2014, 11:22:43 AM

Confirmations

6,234,502

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

ae05056e6808209d563bb98f7176aa307745aad134f16b7d6fcc6ea5ff236fc7

Transactions (4)

Coinbase7053c437f5e3c6…5d02d3ade4220e

1 in → 1 out8.3300 XPM116 B

ANSXnLY2…Sd25TjkD

e4f7cda7a95f6e…5e9ebbaa2bcbc7

1 in → 2 out5.0189 XPM225 B

AecyLB6X…1vQvuHRu AZdo4y7c…KZoWzzS3

9c786c4ff07b2e…465bb69d2fdb20

1 in → 2 out1.6757 XPM225 B

AW9mo9um…6tT5zNeX AGdWVjRk…LFVsqCnK

f175070937929f…4c3ed518cab981

1 in → 2 out1.1146 XPM225 B

Abi8nFbt…bkDhGPuE ARNQQTcv…KJr12Dtj

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.

1.333 × 10¹⁰⁰(101-digit number)

13337523171761055260…33349013542056755199

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

1.333 × 10¹⁰⁰(101-digit number)

13337523171761055260…33349013542056755199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.333 × 10¹⁰⁰(101-digit number)

13337523171761055260…33349013542056755201

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

2.667 × 10¹⁰⁰(101-digit number)

26675046343522110520…66698027084113510399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.667 × 10¹⁰⁰(101-digit number)

26675046343522110520…66698027084113510401

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

5.335 × 10¹⁰⁰(101-digit number)

53350092687044221040…33396054168227020799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.335 × 10¹⁰⁰(101-digit number)

53350092687044221040…33396054168227020801

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

1.067 × 10¹⁰¹(102-digit number)

10670018537408844208…66792108336454041599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.067 × 10¹⁰¹(102-digit number)

10670018537408844208…66792108336454041601

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

2.134 × 10¹⁰¹(102-digit number)

21340037074817688416…33584216672908083199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.134 × 10¹⁰¹(102-digit number)

21340037074817688416…33584216672908083201

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