Home/Chain Registry/Block #2,634,363

Block #2,634,363

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/28/2018, 8:56:24 PM · Difficulty 11.2405 · 4,196,622 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

df520f574e6eff3adc6544bd7bbe36afb8451c18650d355e18b15148190e8992

View on Chainz ↗

Height

#2,634,363

Difficulty

11.240543

Transactions

Size

765 B

Version

Bits

0b3d943d

Nonce

1,043,433,459

Timestamp

4/28/2018, 8:56:24 PM

Confirmations

4,196,622

Merkle Root

656fadb27d89d101688d59648dbd9345f6a934e6eefce02828a1479993e616ad

Transactions (3)

Coinbased844fe96880dcc…61384247792f89

1 in → 1 out7.9200 XPM110 B

APBBzPG8…WQrVdneg

cc6b8e91952414…739a46becbc574

1 in → 2 out7.9800 XPM191 B

AK2ZMJ8u…DURXF6UB AJMrMUVA…XLVBXChy

9cb88bf0e89f9d…9943259e8416ea

2 in → 2 out2.1503 XPM374 B

AaxCraKt…CEBafb4N ARjbw5oN…pxQmhAon

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.

8.327 × 10⁹⁴(95-digit number)

83278575559977842654…43910916487354869760

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

8.327 × 10⁹⁴(95-digit number)

83278575559977842654…43910916487354869759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.327 × 10⁹⁴(95-digit number)

83278575559977842654…43910916487354869761

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

1.665 × 10⁹⁵(96-digit number)

16655715111995568530…87821832974709739519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.665 × 10⁹⁵(96-digit number)

16655715111995568530…87821832974709739521

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

3.331 × 10⁹⁵(96-digit number)

33311430223991137061…75643665949419479039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.331 × 10⁹⁵(96-digit number)

33311430223991137061…75643665949419479041

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

6.662 × 10⁹⁵(96-digit number)

66622860447982274123…51287331898838958079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

6.662 × 10⁹⁵(96-digit number)

66622860447982274123…51287331898838958081

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

1.332 × 10⁹⁶(97-digit number)

13324572089596454824…02574663797677916159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.332 × 10⁹⁶(97-digit number)

13324572089596454824…02574663797677916161

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

2.664 × 10⁹⁶(97-digit number)

26649144179192909649…05149327595355832319

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.

View full Prime Chain Discovery page →

★★★☆☆

Rarity

RareChain length 11

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

Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height

getblockhash 2634363

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data

getblock df520f574e6eff3adc6544bd7bbe36afb8451c18650d355e18b15148190e8992

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help → Debug Window → Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #2,634,363 on Chainz ↗

Block #2,634,363

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