Block #563,836

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/27/2014, 5:29:01 AM · Difficulty 10.9649 · 6,230,948 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e74f29646174b7f98bc1f8eb6f52281a7fe61055cd54c1d25e9fd816bfc70509

View on Chainz ↗

Height

#563,836

Difficulty

10.964871

Transactions

Size

807 B

Version

Bits

0af701ce

Nonce

1,756,673,662

Timestamp

5/27/2014, 5:29:01 AM

Confirmations

6,230,948

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

37d45b4291d95b1b3115ae2b35a59902ca04ce72242cfb2caadbc9bff6431068

Transactions (3)

Coinbase93ba5743f49b72…0b183eea7d039d

1 in → 1 out8.3200 XPM116 B

ANSXnLY2…Sd25TjkD

db2b286668e72f…550f560cfcde02

2 in → 2 out16.6100 XPM374 B

AK1r1S9R…xPmbURu9 ALe73byb…gZoPcGoS

aab3e6f4272c3d…b936562192caed

1 in → 2 out8.2900 XPM226 B

APY6bU6F…oQXHVm48 ATZSzh7F…WG6v1NgN

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.

4.305 × 10⁹⁷(98-digit number)

43052412568690701449…48797192750644460399

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

4.305 × 10⁹⁷(98-digit number)

43052412568690701449…48797192750644460399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.305 × 10⁹⁷(98-digit number)

43052412568690701449…48797192750644460401

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

8.610 × 10⁹⁷(98-digit number)

86104825137381402899…97594385501288920799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

8.610 × 10⁹⁷(98-digit number)

86104825137381402899…97594385501288920801

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

1.722 × 10⁹⁸(99-digit number)

17220965027476280579…95188771002577841599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.722 × 10⁹⁸(99-digit number)

17220965027476280579…95188771002577841601

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

3.444 × 10⁹⁸(99-digit number)

34441930054952561159…90377542005155683199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.444 × 10⁹⁸(99-digit number)

34441930054952561159…90377542005155683201

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

6.888 × 10⁹⁸(99-digit number)

68883860109905122319…80755084010311366399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.888 × 10⁹⁸(99-digit number)

68883860109905122319…80755084010311366401

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

1.377 × 10⁹⁹(100-digit number)

13776772021981024463…61510168020622732799

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