Block #566,696

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/29/2014, 2:28:08 AM · Difficulty 10.9661 · 6,249,908 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe2d4f933341c2a49465b0c94921636c3587e44d6dd3bb2996548a39cc35f00f

View on Chainz ↗

Height

#566,696

Difficulty

10.966059

Transactions

Size

432 B

Version

Bits

0af74fa1

Nonce

794,855,749

Timestamp

5/29/2014, 2:28:08 AM

Confirmations

6,249,908

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

0ab586010afae12848d622b5b6edeec9de40e7c79f339ca9f0df7a0bdb247504

Transactions (2)

Coinbasebdd05597ecf309…da39c968f75277

1 in → 1 out8.3100 XPM116 B

ANSXnLY2…Sd25TjkD

d363739b4357f5…ecd031f7fdac86

1 in → 2 out231.7970 XPM225 B

AdE5MZk4…anqbNuvs AUMUJDNK…yNBumjbQ

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.

1.817 × 10⁹⁷(98-digit number)

18172858501798003882…19534763835597912399

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

1.817 × 10⁹⁷(98-digit number)

18172858501798003882…19534763835597912399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.817 × 10⁹⁷(98-digit number)

18172858501798003882…19534763835597912401

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

3.634 × 10⁹⁷(98-digit number)

36345717003596007764…39069527671195824799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.634 × 10⁹⁷(98-digit number)

36345717003596007764…39069527671195824801

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

7.269 × 10⁹⁷(98-digit number)

72691434007192015528…78139055342391649599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

7.269 × 10⁹⁷(98-digit number)

72691434007192015528…78139055342391649601

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

1.453 × 10⁹⁸(99-digit number)

14538286801438403105…56278110684783299199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.453 × 10⁹⁸(99-digit number)

14538286801438403105…56278110684783299201

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

2.907 × 10⁹⁸(99-digit number)

29076573602876806211…12556221369566598399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.907 × 10⁹⁸(99-digit number)

29076573602876806211…12556221369566598401

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

5.815 × 10⁹⁸(99-digit number)

58153147205753612423…25112442739133196799

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 #566,696

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