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Home/Chain Registry/Block #2,785,623

Block #2,785,623

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/9/2018, 12:43:35 AM Β· Difficulty 11.6719 Β· 4,053,410 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4df791e1b0d34ad7cffed45e795505088659f8d8b3d1071c61065070c60ab7f9
View on Chainz β†—

Difficulty

11.671927

Transactions

1

Size

201 B

Version

2

Bits

0bac036c

Nonce

1,524,436,106

Timestamp

8/9/2018, 12:43:35 AM

Confirmations

4,053,410

Merkle Root

3ed7e0b997a90ab3789b0c318266647aeb29c3aab4a646e1ee014827c91fc638
Transactions (1)
Coinbase3ed7e0b997a90a…014827c91fc638
1 in β†’ 1 out7.3300 XPM110 B
AZtxQr2F…7grUWrUz
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.017 Γ— 10⁹⁷(98-digit number)
10170505153214918563…77401365591660625920
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.017 Γ— 10⁹⁷(98-digit number)
10170505153214918563…77401365591660625919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.017 Γ— 10⁹⁷(98-digit number)
10170505153214918563…77401365591660625921
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.034 Γ— 10⁹⁷(98-digit number)
20341010306429837126…54802731183321251839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.034 Γ— 10⁹⁷(98-digit number)
20341010306429837126…54802731183321251841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.068 Γ— 10⁹⁷(98-digit number)
40682020612859674253…09605462366642503679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.068 Γ— 10⁹⁷(98-digit number)
40682020612859674253…09605462366642503681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
8.136 Γ— 10⁹⁷(98-digit number)
81364041225719348506…19210924733285007359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.136 Γ— 10⁹⁷(98-digit number)
81364041225719348506…19210924733285007361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.627 Γ— 10⁹⁸(99-digit number)
16272808245143869701…38421849466570014719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.627 Γ— 10⁹⁸(99-digit number)
16272808245143869701…38421849466570014721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
3.254 Γ— 10⁹⁸(99-digit number)
32545616490287739402…76843698933140029439
Verify on FactorDB β†—Wolfram Alpha β†—

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 β€” the large number shown above β€” 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 β†’
β˜…β˜…β˜…β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 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 2785623

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 4df791e1b0d34ad7cffed45e795505088659f8d8b3d1071c61065070c60ab7f9

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 β†’ Debug Window β†’ 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 #2,785,623 on Chainz β†—
Circulating Supply:57,956,531 XPMΒ·at block #6,839,032 Β· updates every 60s
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