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Home/Chain Registry/Block #2,634,548

Block #2,634,548

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 10:46:15 PM Β· Difficulty 11.2517 Β· 4,210,535 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
40c6f088248691445a7b9bfbd28cf1b50c19b9a770b57ced15ff4f321e0da093
View on Chainz β†—

Difficulty

11.251668

Transactions

1

Size

199 B

Version

2

Bits

0b406d4d

Nonce

219,629,247

Timestamp

4/28/2018, 10:46:15 PM

Confirmations

4,210,535

Merkle Root

16d919d03863379985b4b72c952c125d67437db8f3bfc96b5e37e5308521c5a6
Transactions (1)
Coinbase16d919d0386337…37e5308521c5a6
1 in β†’ 1 out7.8900 XPM109 B
Adqah8zh…1WwoHJ9t
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.

5.407 Γ— 10⁹⁴(95-digit number)
54078749044772003813…65797649647027486720
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
5.407 Γ— 10⁹⁴(95-digit number)
54078749044772003813…65797649647027486719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.407 Γ— 10⁹⁴(95-digit number)
54078749044772003813…65797649647027486721
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
1.081 Γ— 10⁹⁡(96-digit number)
10815749808954400762…31595299294054973439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.081 Γ— 10⁹⁡(96-digit number)
10815749808954400762…31595299294054973441
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
2.163 Γ— 10⁹⁡(96-digit number)
21631499617908801525…63190598588109946879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.163 Γ— 10⁹⁡(96-digit number)
21631499617908801525…63190598588109946881
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
4.326 Γ— 10⁹⁡(96-digit number)
43262999235817603050…26381197176219893759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.326 Γ— 10⁹⁡(96-digit number)
43262999235817603050…26381197176219893761
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
8.652 Γ— 10⁹⁡(96-digit number)
86525998471635206101…52762394352439787519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.652 Γ— 10⁹⁡(96-digit number)
86525998471635206101…52762394352439787521
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
1.730 Γ— 10⁹⁢(97-digit number)
17305199694327041220…05524788704879575039
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 2634548

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 40c6f088248691445a7b9bfbd28cf1b50c19b9a770b57ced15ff4f321e0da093

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 #2,634,548 on Chainz β†—
Circulating Supply:58,005,091 XPMΒ·at block #6,845,082 Β· updates every 60s
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