Block #2,142,970

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 6/3/2017, 4:36:53 AM · Difficulty 10.8784 · 4,689,960 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

7fee952e63402588cb4ef44fe714ccb6c9a4faa7103d5577ea9ab72b9a585efc

View on Chainz ↗

Height

#2,142,970

Difficulty

10.878388

Transactions

Size

1.08 KB

Version

Bits

0ae0de04

Nonce

475,562,558

Timestamp

6/3/2017, 4:36:53 AM

Confirmations

4,689,960

Mined by

⛏️ P2SHANPfJkCSFGWVJLE7sBEjtnj5wdVr6MAg8L

Merkle Root

a2602098b2609d57de3b23424f5097aa68186bfe6545637f52df4c3e5eeea23b

Transactions (5)

Coinbase51f4a5f9912cc0…d65ad6ffde4680

1 in → 1 out8.4800 XPM109 B

ANPfJkCS…Vr6MAg8L

7563583c113130…ff3969adc6c434

1 in → 2 out182459.9461 XPM227 B

AYMsHst2…HLLQa86T ANnVrL2o…fLHsHBTa

ca210e96e448fe…561a958719e035

1 in → 2 out9999.9900 XPM226 B

AZR9v4B5…YnWtWGYm AboCfGtJ…Smq9tnm3

f3cf28bbd476cf…a05a35caad4efe

1 in → 2 out180134.4261 XPM226 B

AStZvrkV…uUNMtEkB AJ5xHLpg…DPEZhb3Y

4c83fc98faa2a4…f87f0303975b3c

1 in → 2 out9990.0899 XPM226 B

AQZUJcPD…qMvG8T2o ATNNwPCV…id21vw5x

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.

2.040 × 10⁹⁶(97-digit number)

20406563172172785555…91487100965387141119

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

2.040 × 10⁹⁶(97-digit number)

20406563172172785555…91487100965387141119

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.040 × 10⁹⁶(97-digit number)

20406563172172785555…91487100965387141121

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

4.081 × 10⁹⁶(97-digit number)

40813126344345571110…82974201930774282239

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.081 × 10⁹⁶(97-digit number)

40813126344345571110…82974201930774282241

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

8.162 × 10⁹⁶(97-digit number)

81626252688691142221…65948403861548564479

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.162 × 10⁹⁶(97-digit number)

81626252688691142221…65948403861548564481

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

1.632 × 10⁹⁷(98-digit number)

16325250537738228444…31896807723097128959

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.632 × 10⁹⁷(98-digit number)

16325250537738228444…31896807723097128961

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

3.265 × 10⁹⁷(98-digit number)

32650501075476456888…63793615446194257919

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.265 × 10⁹⁷(98-digit number)

32650501075476456888…63793615446194257921

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 #2,142,970

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