Block #2,633,649

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 1:22:12 PM · Difficulty 11.2002 · 4,208,284 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0d794696c964fac445761ab519c42be72ce3a69874011128146063b7ca0498b1

View on Chainz ↗

Height

#2,633,649

Difficulty

11.200247

Transactions

Size

1.43 KB

Version

Bits

0b334366

Nonce

183,153,471

Timestamp

4/28/2018, 1:22:12 PM

Confirmations

4,208,284

Mined by

⛏️ P2SHAehKmwY1ec1qTNf1wtYduvCR3NFNsrfiUB

Merkle Root

8e51808fa8063735485452ffc08c7e775a43779acccbff9d7688d97b6bb96f65

Transactions (4)

Coinbase73aba5b96987bb…36e34a55f438a2

1 in → 1 out8.0000 XPM110 B

AehKmwY1…FNsrfiUB

54cc65685b7ff8…dbbda3dfecfad2

2 in → 6 out1778.4860 XPM510 B

AKgykMUf…Eg79XqTP AU2BRcVZ…gCwc1SKd AQwQCJai…x2rDr9Lo AR75RM6P…cZ5swCt4 AL9E2ASN…Sf6ah74o

02c11ca76e6f36…fdb7599f656b5a

3 in → 2 out11.9900 XPM522 B

AYhLKFHD…iwojd8mb AYuGbfiK…HzMka7bu

9564ffe597c7cc…2b81a4d2a0bc1e

1 in → 2 out5472.0316 XPM227 B

ANhqSXsG…fZcwXDdc AVSSkPKi…uWvzwo2z

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.

2.159 × 10⁹⁶(97-digit number)

21593388750252499797…37138263401838510079

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

2.159 × 10⁹⁶(97-digit number)

21593388750252499797…37138263401838510079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.159 × 10⁹⁶(97-digit number)

21593388750252499797…37138263401838510081

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

4.318 × 10⁹⁶(97-digit number)

43186777500504999595…74276526803677020159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

4.318 × 10⁹⁶(97-digit number)

43186777500504999595…74276526803677020161

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

8.637 × 10⁹⁶(97-digit number)

86373555001009999190…48553053607354040319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

8.637 × 10⁹⁶(97-digit number)

86373555001009999190…48553053607354040321

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

1.727 × 10⁹⁷(98-digit number)

17274711000201999838…97106107214708080639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.727 × 10⁹⁷(98-digit number)

17274711000201999838…97106107214708080641

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

3.454 × 10⁹⁷(98-digit number)

34549422000403999676…94212214429416161279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

3.454 × 10⁹⁷(98-digit number)

34549422000403999676…94212214429416161281

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

6.909 × 10⁹⁷(98-digit number)

69098844000807999352…88424428858832322559

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 #2,633,649

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