Block #2,088,147

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/26/2017, 3:41:24 AM · Difficulty 10.8752 · 4,743,147 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

ecffbec05b7f62bcdc93f930e7269444feb8292ac9add7e9d57dc863b87bc299

View on Chainz ↗

Height

#2,088,147

Difficulty

10.875196

Transactions

Size

1.95 KB

Version

Bits

0ae00cd5

Nonce

1,251,050,470

Timestamp

4/26/2017, 3:41:24 AM

Confirmations

4,743,147

Mined by

⛏️ P2SHAeXfnUHKP8rGnSMecSo6FxaXWhEBH8JgbK

Merkle Root

90ff55e94c000110f62e88d9cd31b17627a36fe39eea3e0ee82be045095499f8

Transactions (5)

Coinbase9f376a8f4e51e4…cdd0cd9f926693

1 in → 1 out8.4900 XPM109 B

AeXfnUHK…EBH8JgbK

3609fade11be8d…892e702df8abe2

7 in → 2 out3025.4175 XPM1.09 KB

AQYPwhui…ygwqYt1Y ANh31Mv9…rTcekU2G

ace0bd9972be3e…4d3f7e14d4e36f

1 in → 2 out494.9900 XPM227 B

Aep9jLtU…vmBHLtuS AJDJ95ED…Yee8KSP9

9c3852aa98100f…42cef3a3dd9721

1 in → 2 out2.4322 XPM227 B

AVLQvrDT…LicMPPXc AMCPVCXH…L83RFHx8

56b15ab48e3f97…8e8dbec0e69755

1 in → 2 out2.1040 XPM226 B

AQ8iitEN…Z5v6jQju AYVBmLey…e5tVN1ar

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.

2.091 × 10⁹⁷(98-digit number)

20917226216398107448…34580448813815398399

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

2.091 × 10⁹⁷(98-digit number)

20917226216398107448…34580448813815398399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.091 × 10⁹⁷(98-digit number)

20917226216398107448…34580448813815398401

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

4.183 × 10⁹⁷(98-digit number)

41834452432796214896…69160897627630796799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.183 × 10⁹⁷(98-digit number)

41834452432796214896…69160897627630796801

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

8.366 × 10⁹⁷(98-digit number)

83668904865592429793…38321795255261593599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.366 × 10⁹⁷(98-digit number)

83668904865592429793…38321795255261593601

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

1.673 × 10⁹⁸(99-digit number)

16733780973118485958…76643590510523187199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.673 × 10⁹⁸(99-digit number)

16733780973118485958…76643590510523187201

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

3.346 × 10⁹⁸(99-digit number)

33467561946236971917…53287181021046374399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.346 × 10⁹⁸(99-digit number)

33467561946236971917…53287181021046374401

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #2,088,147

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