Block #566,718

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/29/2014, 2:51:35 AM · Difficulty 10.9661 · 6,241,414 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

a67a8d7feaa792b8efea8b3c7e3e773b4ed8f255776e69ac5336b0feb8721505

View on Chainz ↗

Height

#566,718

Difficulty

10.966052

Transactions

Size

661 B

Version

Bits

0af74f31

Nonce

269,595,286

Timestamp

5/29/2014, 2:51:35 AM

Confirmations

6,241,414

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

d68fa844a6db58ec2497c676c0505a30c0a8b0dfd87dfd4ed6a119dc1059fdb2

Transactions (3)

Coinbaseea3d5fc845f6b3…0ac8111fbc6e41

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

901a2b46657665…a36c38c39cd738

1 in → 2 out6.2578 XPM227 B

AG8u7ddV…cU5QJSqk Af48BojK…8tfFMLpu

230ba6d0a21a94…b0b522b66e8d8f

1 in → 2 out1.2721 XPM225 B

AS9ZCvju…bu3NEFwZ AYHpLE7c…sodvdPZ4

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.

5.456 × 10¹⁰⁰(101-digit number)

54567847512591124825…60512021540723711999

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

5.456 × 10¹⁰⁰(101-digit number)

54567847512591124825…60512021540723711999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.456 × 10¹⁰⁰(101-digit number)

54567847512591124825…60512021540723712001

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

1.091 × 10¹⁰¹(102-digit number)

10913569502518224965…21024043081447423999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.091 × 10¹⁰¹(102-digit number)

10913569502518224965…21024043081447424001

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

2.182 × 10¹⁰¹(102-digit number)

21827139005036449930…42048086162894847999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.182 × 10¹⁰¹(102-digit number)

21827139005036449930…42048086162894848001

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

4.365 × 10¹⁰¹(102-digit number)

43654278010072899860…84096172325789695999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.365 × 10¹⁰¹(102-digit number)

43654278010072899860…84096172325789696001

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

8.730 × 10¹⁰¹(102-digit number)

87308556020145799720…68192344651579391999

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.730 × 10¹⁰¹(102-digit number)

87308556020145799720…68192344651579392001

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

1.746 × 10¹⁰²(103-digit number)

17461711204029159944…36384689303158783999

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

Block #566,718

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