Block #2,098,686

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/3/2017, 7:51:04 PM · Difficulty 10.8623 · 4,735,081 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

c8df61a27806a3406c2127bd2762f6aaa8dfbf3040905026ee5fb7e279d721dc

View on Chainz ↗

Height

#2,098,686

Difficulty

10.862266

Transactions

Size

1.88 KB

Version

Bits

0adcbd78

Nonce

235,561,060

Timestamp

5/3/2017, 7:51:04 PM

Confirmations

4,735,081

Mined by

⛏️ P2SHANXVRmtbtpP2bpfWtd6mnTJEvLUWzHjy6n

Merkle Root

64912514edb4c198dd3da2a69c87cc87989a6b65829df18b36c7f487088dfbed

Transactions (3)

Coinbased73cccf8ad826d…642cfe1ea8c39c

1 in → 1 out8.4900 XPM109 B

ANXVRmtb…UWzHjy6n

2996fc0b608791…cc8f6469347c50

1 in → 2 out8.4300 XPM193 B

AXCz3i15…bd3tZodd AMTS2rMD…nazZ3gMJ

04d6a98bb9a314…b9b9c576391b51

11 in → 2 out50.4108 XPM1.50 KB

ARezZb4y…FxP7ivbi AMyh55w9…ftY4wb3W

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.

1.118 × 10⁹⁴(95-digit number)

11180674464320480944…85602744107853557759

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

1.118 × 10⁹⁴(95-digit number)

11180674464320480944…85602744107853557759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.118 × 10⁹⁴(95-digit number)

11180674464320480944…85602744107853557761

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

2.236 × 10⁹⁴(95-digit number)

22361348928640961888…71205488215707115519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.236 × 10⁹⁴(95-digit number)

22361348928640961888…71205488215707115521

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

4.472 × 10⁹⁴(95-digit number)

44722697857281923777…42410976431414231039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.472 × 10⁹⁴(95-digit number)

44722697857281923777…42410976431414231041

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

8.944 × 10⁹⁴(95-digit number)

89445395714563847554…84821952862828462079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

8.944 × 10⁹⁴(95-digit number)

89445395714563847554…84821952862828462081

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

1.788 × 10⁹⁵(96-digit number)

17889079142912769510…69643905725656924159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.788 × 10⁹⁵(96-digit number)

17889079142912769510…69643905725656924161

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 #2,098,686

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