Block #2,099,515

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 5/4/2017, 1:28:11 PM · Difficulty 10.8559 · 4,743,409 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

3d78c3cb4f97d5e2a8fe8de55844cf33b55790060bcdcf9aec9977cfd4f8a6a0

View on Chainz ↗

Height

#2,099,515

Difficulty

10.855924

Transactions

Size

723 B

Version

Bits

0adb1dd5

Nonce

142,358,596

Timestamp

5/4/2017, 1:28:11 PM

Confirmations

4,743,409

Mined by

⛏️ P2SHAJ6FRJApM1jKtSPe6wvkMSm1oYowCseEvb

Merkle Root

b21f4fc2e404ac3cea6cd73d4f1fd0c29fd19f5d7ff9d481e72c8a7faeee557f

Transactions (2)

Coinbase90b50181420c4f…c7449ddf017023

1 in → 1 out8.4900 XPM110 B

AJ6FRJAp…owCseEvb

27ffb57ec7cedf…518950f51c7246

3 in → 2 out311.7700 XPM523 B

ASH8nfwU…Zmrj5acC ATkYRPjb…8y5c21Ay

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.

5.481 × 10⁹⁵(96-digit number)

54812832726572182801…01999388422665986559

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

5.481 × 10⁹⁵(96-digit number)

54812832726572182801…01999388422665986559

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.481 × 10⁹⁵(96-digit number)

54812832726572182801…01999388422665986561

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

1.096 × 10⁹⁶(97-digit number)

10962566545314436560…03998776845331973119

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.096 × 10⁹⁶(97-digit number)

10962566545314436560…03998776845331973121

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

2.192 × 10⁹⁶(97-digit number)

21925133090628873120…07997553690663946239

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.192 × 10⁹⁶(97-digit number)

21925133090628873120…07997553690663946241

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

4.385 × 10⁹⁶(97-digit number)

43850266181257746241…15995107381327892479

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.385 × 10⁹⁶(97-digit number)

43850266181257746241…15995107381327892481

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

8.770 × 10⁹⁶(97-digit number)

87700532362515492483…31990214762655784959

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

8.770 × 10⁹⁶(97-digit number)

87700532362515492483…31990214762655784961

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 #2,099,515

Cookie Preferences