Block #2,138,498

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2017, 10:48:33 PM · Difficulty 10.8829 · 4,672,605 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

e391ed16ab295c480b56edecfb062981ff8c41f9b324b288e7d571bc93877aa4

View on Chainz ↗

Height

#2,138,498

Difficulty

10.882916

Transactions

Size

3.68 KB

Version

Bits

0ae206cd

Nonce

1,156,675,163

Timestamp

5/30/2017, 10:48:33 PM

Confirmations

4,672,605

Mined by

⛏️ P2SHAXR5k14tU7pVo4eCrwAFDyneeAoFEyAbxz

Merkle Root

7fa7fe35adb63b502fd8b9463500dc327cf9a47a36d58f44018804e5d58cc0f3

Transactions (4)

Coinbasea8f3c4aa389d36…ea25b7be65ddd7

1 in → 1 out8.4800 XPM109 B

AXR5k14t…oFEyAbxz

521926a7f75e20…33d4ec999f0210

1 in → 2 out75563.2749 XPM226 B

AN1EGxhR…uTWDBrmn AGMPuH9Q…BXCrPRUw

88a1c2b9cd5a23…d1154bed34d158

18 in → 1 out726.8354 XPM2.64 KB

AVB8Kqgj…zUanL8Tf

d7fbe9fec6bf33…10da2ae590eb58

4 in → 2 out15.8386 XPM636 B

AbwhbHLD…NxTepUUF AHbyumek…ry7WXVsp

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.

1.652 × 10⁹⁵(96-digit number)

16521451224348471596…71387041864196757759

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

1.652 × 10⁹⁵(96-digit number)

16521451224348471596…71387041864196757759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.652 × 10⁹⁵(96-digit number)

16521451224348471596…71387041864196757761

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

3.304 × 10⁹⁵(96-digit number)

33042902448696943192…42774083728393515519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

3.304 × 10⁹⁵(96-digit number)

33042902448696943192…42774083728393515521

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

6.608 × 10⁹⁵(96-digit number)

66085804897393886384…85548167456787031039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

6.608 × 10⁹⁵(96-digit number)

66085804897393886384…85548167456787031041

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

1.321 × 10⁹⁶(97-digit number)

13217160979478777276…71096334913574062079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.321 × 10⁹⁶(97-digit number)

13217160979478777276…71096334913574062081

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

2.643 × 10⁹⁶(97-digit number)

26434321958957554553…42192669827148124159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.643 × 10⁹⁶(97-digit number)

26434321958957554553…42192669827148124161

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 #2,138,498

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