Block #2,115,600

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/14/2017, 9:17:53 AM · Difficulty 10.9023 · 4,726,042 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

dc8e8485c77117bf94d70c138cdc4b43643f77424fb7bfc614f74447c6dbc1b1

View on Chainz ↗

Height

#2,115,600

Difficulty

10.902317

Transactions

Size

1.63 KB

Version

Bits

0ae6fe44

Nonce

449,180,243

Timestamp

5/14/2017, 9:17:53 AM

Confirmations

4,726,042

Mined by

⛏️ P2SHAY9337LCWmpLzk52ZbRdLpTDp8XZQ4HEiT

Merkle Root

1c77c724e944bdc78501d474eef48b0f1e5d6f1249438dc6cc10dfa348e9f22e

Transactions (4)

Coinbase18c334210c4fbf…af358a4d19fcfd

1 in → 1 out8.4300 XPM109 B

AY9337LC…XZQ4HEiT

d6aaac052ed875…39dd8fec37a23d

2 in → 2 out1531.5908 XPM374 B

AUfiNpNR…r4iERJXe Aepsh78S…8KTQCWCJ

e114f7f512c95a…4ca15306891c78

7 in → 2 out58.8600 XPM874 B

AUaY5CnA…eTzWHa8D Ab2QPysc…MAkKxcKV

2327c69e0cf310…879c62efc4794c

1 in → 2 out6.5399 XPM225 B

AGbm9W17…Jvw6eg2t AM4cFcYP…as3jcpGY

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.

4.547 × 10⁹³(94-digit number)

45476514248624447651…73093157403863144559

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

4.547 × 10⁹³(94-digit number)

45476514248624447651…73093157403863144559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

4.547 × 10⁹³(94-digit number)

45476514248624447651…73093157403863144561

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

9.095 × 10⁹³(94-digit number)

90953028497248895302…46186314807726289119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

9.095 × 10⁹³(94-digit number)

90953028497248895302…46186314807726289121

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

1.819 × 10⁹⁴(95-digit number)

18190605699449779060…92372629615452578239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.819 × 10⁹⁴(95-digit number)

18190605699449779060…92372629615452578241

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

3.638 × 10⁹⁴(95-digit number)

36381211398899558121…84745259230905156479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.638 × 10⁹⁴(95-digit number)

36381211398899558121…84745259230905156481

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

7.276 × 10⁹⁴(95-digit number)

72762422797799116242…69490518461810312959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

7.276 × 10⁹⁴(95-digit number)

72762422797799116242…69490518461810312961

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 #2,115,600

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