Block #2,587,982

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/27/2018, 6:42:43 AM · Difficulty 11.3176 · 4,256,596 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

890f1c28f56a2b87f96280be8ab246c5bbedd1a72adb32d90f7720c0c646008a

View on Chainz ↗

Height

#2,587,982

Difficulty

11.317597

Transactions

Size

1.13 KB

Version

Bits

0b514e03

Nonce

31,000,096

Timestamp

3/27/2018, 6:42:43 AM

Confirmations

4,256,596

Mined by

⛏️ P2SHAW7JF18SGPPrkxnTAVdReEwb6kUQXeKGmR

Merkle Root

82f901c2db3bfd4b62b27bb42ea32ac304000a47327d3ee0f9bbbc9d43f74e85

Transactions (4)

Coinbaseef9f5890e14ee4…b2f3469183ff75

1 in → 1 out7.8200 XPM110 B

AW7JF18S…UQXeKGmR

3ab13635b22d38…0299e111981c62

2 in → 2 out15.8300 XPM305 B

AQSDgFjc…TFSZymzv AMwmR7Md…T1b83Bab

3692b58b319cd7…cab0f507714989

2 in → 2 out15.8300 XPM306 B

ALkfs46B…MLdMZtzF AM6XD26m…RcphfPC1

88000d5164e7ab…e19cf76cde68f9

2 in → 2 out10.5300 XPM341 B

ARVxy78i…WJVP7dyZ AW3QZZmg…j2rGjUkp

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.

7.088 × 10⁹⁴(95-digit number)

70887032994619551332…80203116195990138879

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

7.088 × 10⁹⁴(95-digit number)

70887032994619551332…80203116195990138879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

7.088 × 10⁹⁴(95-digit number)

70887032994619551332…80203116195990138881

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

1.417 × 10⁹⁵(96-digit number)

14177406598923910266…60406232391980277759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.417 × 10⁹⁵(96-digit number)

14177406598923910266…60406232391980277761

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

2.835 × 10⁹⁵(96-digit number)

28354813197847820532…20812464783960555519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.835 × 10⁹⁵(96-digit number)

28354813197847820532…20812464783960555521

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

5.670 × 10⁹⁵(96-digit number)

56709626395695641065…41624929567921111039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.670 × 10⁹⁵(96-digit number)

56709626395695641065…41624929567921111041

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

1.134 × 10⁹⁶(97-digit number)

11341925279139128213…83249859135842222079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.134 × 10⁹⁶(97-digit number)

11341925279139128213…83249859135842222081

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

2.268 × 10⁹⁶(97-digit number)

22683850558278256426…66499718271684444159

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 #2,587,982

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