Block #2,089,528

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 4/27/2017, 2:20:22 AM · Difficulty 10.8758 · 4,726,561 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d96b8b94fcea2cc278ed87d70120b5321505000e5e9e115d213f57f5e33ce25b

View on Chainz ↗

Height

#2,089,528

Difficulty

10.875828

Transactions

Size

1.79 KB

Version

Bits

0ae03648

Nonce

1,792,285,040

Timestamp

4/27/2017, 2:20:22 AM

Confirmations

4,726,561

Mined by

⛏️ P2SHAMQB28wvHCTfpUF8t1u1SEdgLbMnJ8B85W

Merkle Root

827b9f139c259c8e8999bd0484cae50ada9493e66dfa7401471adad02dcfa879

Transactions (3)

Coinbase46e03ee4324b8e…a05159cc344b32

1 in → 1 out8.4800 XPM109 B

AMQB28wv…MnJ8B85W

e41b3bf7179cea…71934288ff9aeb

4 in → 2 out5422.9258 XPM671 B

AcF4MCPV…VRzZseB4 AYTxq7wZ…d6FHuQMd

30a2cc6d558369…29397c63ff9fbd

6 in → 2 out5761.0137 XPM964 B

AYTxq7wZ…d6FHuQMd AKEwqHXv…2egsTtST

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.

9.989 × 10⁹⁴(95-digit number)

99898534431510504710…97593228240321070399

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

9.989 × 10⁹⁴(95-digit number)

99898534431510504710…97593228240321070399

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.989 × 10⁹⁴(95-digit number)

99898534431510504710…97593228240321070401

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

1.997 × 10⁹⁵(96-digit number)

19979706886302100942…95186456480642140799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.997 × 10⁹⁵(96-digit number)

19979706886302100942…95186456480642140801

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

3.995 × 10⁹⁵(96-digit number)

39959413772604201884…90372912961284281599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.995 × 10⁹⁵(96-digit number)

39959413772604201884…90372912961284281601

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

7.991 × 10⁹⁵(96-digit number)

79918827545208403768…80745825922568563199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.991 × 10⁹⁵(96-digit number)

79918827545208403768…80745825922568563201

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

1.598 × 10⁹⁶(97-digit number)

15983765509041680753…61491651845137126399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.598 × 10⁹⁶(97-digit number)

15983765509041680753…61491651845137126401

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 #2,089,528

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