Block #574,574

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/3/2014, 10:17:20 AM · Difficulty 10.9677 · 6,226,760 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c2b2c7c4c55c6ed8f439cdcb4dc95c2cca5e489eb1dbf84eeebd4668bfbdb597

View on Chainz ↗

Height

#574,574

Difficulty

10.967692

Transactions

Size

588 B

Version

Bits

0af7bab0

Nonce

51,560

Timestamp

6/3/2014, 10:17:20 AM

Confirmations

6,226,760

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

6fd16358643f00296aa79a4ddee8a94731aa68dd95e3d379709d72fb619fc520

Transactions (3)

Coinbase71776898becc24…f5211807858838

1 in → 1 out8.3200 XPM110 B

AeKNrjNj…1NEq95Ta

b84e8c07bb9ce3…c84d87b571100c

1 in → 1 out209.9900 XPM192 B

AMvDEhZv…V5YvJTWj

0091e5f8461021…7e05b4de9e0526

1 in → 1 out0.3230 XPM192 B

AGXFqSyj…FxquNuxH

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.

3.382 × 10¹⁰³(104-digit number)

33828563683144441393…51496040711156019199

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

3.382 × 10¹⁰³(104-digit number)

33828563683144441393…51496040711156019199

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.382 × 10¹⁰³(104-digit number)

33828563683144441393…51496040711156019201

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

6.765 × 10¹⁰³(104-digit number)

67657127366288882787…02992081422312038399

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

6.765 × 10¹⁰³(104-digit number)

67657127366288882787…02992081422312038401

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

1.353 × 10¹⁰⁴(105-digit number)

13531425473257776557…05984162844624076799

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.353 × 10¹⁰⁴(105-digit number)

13531425473257776557…05984162844624076801

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

2.706 × 10¹⁰⁴(105-digit number)

27062850946515553114…11968325689248153599

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.706 × 10¹⁰⁴(105-digit number)

27062850946515553114…11968325689248153601

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

5.412 × 10¹⁰⁴(105-digit number)

54125701893031106229…23936651378496307199

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

5.412 × 10¹⁰⁴(105-digit number)

54125701893031106229…23936651378496307201

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

1.082 × 10¹⁰⁵(106-digit number)

10825140378606221245…47873302756992614399

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