Block #2,721,557

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/26/2018, 1:37:06 AM · Difficulty 11.6161 · 4,111,658 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6957c1413e45b4076df2f46116c43eeaebd8d2861ada39d564ced196d210adf

View on Chainz ↗

Height

#2,721,557

Difficulty

11.616098

Transactions

Size

1.30 KB

Version

Bits

0b9db895

Nonce

654,570,981

Timestamp

6/26/2018, 1:37:06 AM

Confirmations

4,111,658

Mined by

⛏️ P2SHAZtxQr2FMR4PURkVAAuK17mDJ17grUWrUz

Merkle Root

3814591b4168611ea6874db5988b186b7c8e55ae09c7d90756a9508b0b217ca0

Transactions (4)

Coinbase97ee731fdd1423…268fe9a1847af5

1 in → 1 out7.4300 XPM110 B

AZtxQr2F…7grUWrUz

cc5eeadb8dac46…88bf82a3be01fb

2 in → 2 out14.8700 XPM307 B

AVZY7fRQ…voPLHzeJ ATkPigJz…2LyNXQRx

9b0a30ef937909…8acf390c468e74

2 in → 2 out14.7900 XPM306 B

AM7HYByC…YhcyJvAq AYBL42jS…rpLSNCjL

8f43e37660aee7…bc83b5562fcb31

3 in → 2 out11.8700 XPM523 B

ASxkQAv4…mZ45Sf5W AQzJf9MX…32Uh5Hb3

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.

9.080 × 10⁹⁴(95-digit number)

90808385466617823563…27682685913418561279

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

9.080 × 10⁹⁴(95-digit number)

90808385466617823563…27682685913418561279

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.080 × 10⁹⁴(95-digit number)

90808385466617823563…27682685913418561281

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

1.816 × 10⁹⁵(96-digit number)

18161677093323564712…55365371826837122559

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.816 × 10⁹⁵(96-digit number)

18161677093323564712…55365371826837122561

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

3.632 × 10⁹⁵(96-digit number)

36323354186647129425…10730743653674245119

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.632 × 10⁹⁵(96-digit number)

36323354186647129425…10730743653674245121

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

7.264 × 10⁹⁵(96-digit number)

72646708373294258850…21461487307348490239

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.264 × 10⁹⁵(96-digit number)

72646708373294258850…21461487307348490241

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

1.452 × 10⁹⁶(97-digit number)

14529341674658851770…42922974614696980479

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.452 × 10⁹⁶(97-digit number)

14529341674658851770…42922974614696980481

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

2.905 × 10⁹⁶(97-digit number)

29058683349317703540…85845949229393960959

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,721,557

Cookie Preferences