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Block #2,638,882

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 4/30/2018, 10:54:57 AM · Difficulty 11.5131 · 4,200,153 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d88b40742152f9770cbca804f05efb980854516acd255c4c17b30532ed81c3ae

View on Chainz ↗

Height

#2,638,882

Difficulty

11.513130

Transactions

Size

572 B

Version

Bits

0b835c77

Nonce

251,054,320

Timestamp

4/30/2018, 10:54:57 AM

Confirmations

4,200,153

Merkle Root

2a3119b0adb33e754fc776fcad011f47a78e9d88842d0f6261d288604f0f178d

Transactions (2)

Coinbase5df84da9448d60…a8a034b1ac653d

1 in → 1 out7.5500 XPM109 B

AKKppueh…cY8dv1Gi

0f6821b58e93c9…58849033f1676a

2 in → 2 out9.9765 XPM372 B

AcxLeUjj…vC4cELBE AS4khYnr…fh8mQeBq

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.

1.131 × 10⁹⁶(97-digit number)

11312569337982868561…62323033158030032960

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

1.131 × 10⁹⁶(97-digit number)

11312569337982868561…62323033158030032959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.131 × 10⁹⁶(97-digit number)

11312569337982868561…62323033158030032961

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

2.262 × 10⁹⁶(97-digit number)

22625138675965737122…24646066316060065919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.262 × 10⁹⁶(97-digit number)

22625138675965737122…24646066316060065921

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

4.525 × 10⁹⁶(97-digit number)

45250277351931474245…49292132632120131839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

4.525 × 10⁹⁶(97-digit number)

45250277351931474245…49292132632120131841

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

9.050 × 10⁹⁶(97-digit number)

90500554703862948490…98584265264240263679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

9.050 × 10⁹⁶(97-digit number)

90500554703862948490…98584265264240263681

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

1.810 × 10⁹⁷(98-digit number)

18100110940772589698…97168530528480527359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.810 × 10⁹⁷(98-digit number)

18100110940772589698…97168530528480527361

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

3.620 × 10⁹⁷(98-digit number)

36200221881545179396…94337061056961054719

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 2638882

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 d88b40742152f9770cbca804f05efb980854516acd255c4c17b30532ed81c3ae

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 #2,638,882 on Chainz ↗

Block #2,638,882

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