Block #2,097,923

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2017, 2:57:58 AM · Difficulty 10.8689 · 4,742,770 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

6813ffd04d8fcc46888e0be733ebd7092eec829bedb2f31b82c14d9a0bfa1d3f

View on Chainz ↗

Height

#2,097,923

Difficulty

10.868913

Transactions

Size

2.64 KB

Version

Bits

0ade7117

Nonce

1,924,551,637

Timestamp

5/3/2017, 2:57:58 AM

Confirmations

4,742,770

Mined by

⛏️ P2SHAeKSgzibUQ66SWcqLoB9FnJofKVuKtEJ7U

Merkle Root

66271a90ccd12d5a17c94a8696e55b5abe63c7998d7aa9319b396445b46aacc9

Transactions (4)

Coinbased0f057193d0def…fac2554ed370d7

1 in → 1 out8.4900 XPM109 B

AeKSgzib…VuKtEJ7U

8c0be77cbb0296…9fc13a9c0f9315

4 in → 1 out110.0000 XPM638 B

AVaj27ki…Ntfy4Rjn

4ba5ca3fe66e27…99e75e5401cd35

8 in → 1 out211.0000 XPM1.20 KB

AVaj27ki…Ntfy4Rjn

ef843a7641ddc0…e2f9c624951a48

4 in → 1 out111.0000 XPM637 B

AVaj27ki…Ntfy4Rjn

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.

6.944 × 10⁹⁴(95-digit number)

69444436910609323397…90738062166655559679

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

6.944 × 10⁹⁴(95-digit number)

69444436910609323397…90738062166655559679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.944 × 10⁹⁴(95-digit number)

69444436910609323397…90738062166655559681

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

1.388 × 10⁹⁵(96-digit number)

13888887382121864679…81476124333311119359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.388 × 10⁹⁵(96-digit number)

13888887382121864679…81476124333311119361

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

2.777 × 10⁹⁵(96-digit number)

27777774764243729359…62952248666622238719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.777 × 10⁹⁵(96-digit number)

27777774764243729359…62952248666622238721

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

5.555 × 10⁹⁵(96-digit number)

55555549528487458718…25904497333244477439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.555 × 10⁹⁵(96-digit number)

55555549528487458718…25904497333244477441

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

1.111 × 10⁹⁶(97-digit number)

11111109905697491743…51808994666488954879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.111 × 10⁹⁶(97-digit number)

11111109905697491743…51808994666488954881

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 #2,097,923

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