Block #2,137,502

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/30/2017, 2:34:13 AM · Difficulty 10.8878 · 4,707,687 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d01102ed360d7e74854a828df09c1aedf827674708a28d5db170c393e3e32c45

View on Chainz ↗

Height

#2,137,502

Difficulty

10.887831

Transactions

Size

878 B

Version

Bits

0ae348de

Nonce

1,166,041,991

Timestamp

5/30/2017, 2:34:13 AM

Confirmations

4,707,687

Mined by

⛏️ P2SHAapYiGGVzg1SKXBqMhBtcssMu1THWRyaFv

Merkle Root

232e6e793b501bb43de19af80ecb33f1027e1d214a809a4d2002d448ea333da7

Transactions (4)

Coinbase8f48bb85cf52f4…863846146cddbc

1 in → 1 out8.4500 XPM109 B

AapYiGGV…THWRyaFv

bf3f3824c0fbbb…4f34ec3307ce63

1 in → 2 out48263.4563 XPM227 B

AcyjGv5U…SWaM5Lg7 Aa8iPEC8…xyKYCCRy

b448bd077184e7…605c0e2555dba2

1 in → 2 out43150.1656 XPM226 B

ATcGjH3N…ydphKrR3 AYr7U671…gnmYN2iu

cfddee79588f1c…c6688e2bf29603

1 in → 2 out36200.6733 XPM226 B

AZe7DnB2…JRwf42cw ARfSnJ57…UMRhVwND

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.

1.242 × 10⁹⁴(95-digit number)

12422219951214527318…36626798685066141679

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

1.242 × 10⁹⁴(95-digit number)

12422219951214527318…36626798685066141679

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.242 × 10⁹⁴(95-digit number)

12422219951214527318…36626798685066141681

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

2.484 × 10⁹⁴(95-digit number)

24844439902429054637…73253597370132283359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.484 × 10⁹⁴(95-digit number)

24844439902429054637…73253597370132283361

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

4.968 × 10⁹⁴(95-digit number)

49688879804858109274…46507194740264566719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.968 × 10⁹⁴(95-digit number)

49688879804858109274…46507194740264566721

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

9.937 × 10⁹⁴(95-digit number)

99377759609716218548…93014389480529133439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.937 × 10⁹⁴(95-digit number)

99377759609716218548…93014389480529133441

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

1.987 × 10⁹⁵(96-digit number)

19875551921943243709…86028778961058266879

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.987 × 10⁹⁵(96-digit number)

19875551921943243709…86028778961058266881

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 #2,137,502

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