Block #2,162,764

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/16/2017, 6:03:15 AM · Difficulty 10.9006 · 4,634,089 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

80cee754610a5e4c6840412897fdd8d4394c55ceaf7de71c4ab56e875dbeb112

View on Chainz ↗

Height

#2,162,764

Difficulty

10.900618

Transactions

Size

879 B

Version

Bits

0ae68ee9

Nonce

278,326,779

Timestamp

6/16/2017, 6:03:15 AM

Confirmations

4,634,089

Mined by

⛏️ P2SHAMPuqCZTCPkYzg5yj5Z9rHd6rChcEzQTi8

Merkle Root

84a1c6a5735b2c82781935720a3169274f1e7900e5b17feaaf5c327eadccde1c

Transactions (4)

Coinbase9f3f35eca084d7…3b165f2556a135

1 in → 1 out8.4300 XPM110 B

AMPuqCZT…hcEzQTi8

9a2e09d83ef7a3…535abc9f9ea077

1 in → 2 out4.3800 XPM225 B

AP2GxFDi…MZQBdSYt AKi6WU6d…Y6v1gzse

b1ec0977c0a5f9…3bc0ecb68ad7aa

1 in → 2 out4.3800 XPM226 B

ANn3UmGS…Qj615a9T AL9CLiGb…sBN8x6ct

90d5bfd640852a…43b7b21af47f88

1 in → 2 out4.3800 XPM227 B

AN7SyZXo…McSmJn39 ANVrHE4T…sn55J2RS

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.

2.721 × 10⁹⁷(98-digit number)

27214382266068748842…39677264107502018559

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

2.721 × 10⁹⁷(98-digit number)

27214382266068748842…39677264107502018559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.721 × 10⁹⁷(98-digit number)

27214382266068748842…39677264107502018561

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

5.442 × 10⁹⁷(98-digit number)

54428764532137497685…79354528215004037119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.442 × 10⁹⁷(98-digit number)

54428764532137497685…79354528215004037121

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

1.088 × 10⁹⁸(99-digit number)

10885752906427499537…58709056430008074239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.088 × 10⁹⁸(99-digit number)

10885752906427499537…58709056430008074241

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

2.177 × 10⁹⁸(99-digit number)

21771505812854999074…17418112860016148479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.177 × 10⁹⁸(99-digit number)

21771505812854999074…17418112860016148481

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

4.354 × 10⁹⁸(99-digit number)

43543011625709998148…34836225720032296959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.354 × 10⁹⁸(99-digit number)

43543011625709998148…34836225720032296961

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

8.708 × 10⁹⁸(99-digit number)

87086023251419996296…69672451440064593919

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