Block #2,644,586

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 5/2/2018, 1:37:56 PM · Difficulty 11.7130 · 4,199,877 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

fe213db8b8ab2b4728975cdebb8271164734da8cc5ae79f9f64fecef2fb60b2b

View on Chainz ↗

Height

#2,644,586

Difficulty

11.712974

Transactions

Size

880 B

Version

Bits

0bb6856f

Nonce

699,577,141

Timestamp

5/2/2018, 1:37:56 PM

Confirmations

4,199,877

Mined by

⛏️ P2SHAXAazEx71KriBpyzf8V3eFfFnFdE7GyN2L

Merkle Root

c71201a3245d6837598319bce591c3996783b127f1242943f6ae954bb0862e14

Transactions (4)

Coinbaseb732f6a2a2ce6e…25d3dac0ebeb66

1 in → 1 out7.3100 XPM110 B

AXAazEx7…dE7GyN2L

11d88cbbbe91ff…6b43fcdf355c33

1 in → 2 out6.3616 XPM226 B

AaxCraKt…CEBafb4N ATE5dGvL…qpsDBPZ1

44cb39aca85271…cbfcc4e05074df

1 in → 2 out6.3400 XPM226 B

AYDuNsYz…Mtn61d6g AYGotN8o…pnCUVBsf

3668af877c33ef…3511b4dc690ce8

1 in → 2 out6.3557 XPM227 B

AKpcYo9x…uuSmd18X ARNe3C8D…KfGUT8YN

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.

1.133 × 10⁹⁶(97-digit number)

11331517493825860603…79918420633446766079

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

1.133 × 10⁹⁶(97-digit number)

11331517493825860603…79918420633446766079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.133 × 10⁹⁶(97-digit number)

11331517493825860603…79918420633446766081

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

2.266 × 10⁹⁶(97-digit number)

22663034987651721206…59836841266893532159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.266 × 10⁹⁶(97-digit number)

22663034987651721206…59836841266893532161

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

4.532 × 10⁹⁶(97-digit number)

45326069975303442412…19673682533787064319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.532 × 10⁹⁶(97-digit number)

45326069975303442412…19673682533787064321

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

9.065 × 10⁹⁶(97-digit number)

90652139950606884825…39347365067574128639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.065 × 10⁹⁶(97-digit number)

90652139950606884825…39347365067574128641

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

1.813 × 10⁹⁷(98-digit number)

18130427990121376965…78694730135148257279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.813 × 10⁹⁷(98-digit number)

18130427990121376965…78694730135148257281

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

3.626 × 10⁹⁷(98-digit number)

36260855980242753930…57389460270296514559

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 #2,644,586

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