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Home/Chain Registry/Block #2,634,397

Block #2,634,397

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 9:14:20 PM Β· Difficulty 11.2429 Β· 4,196,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
25871d87ba1cad6b470367876376d10fead74c978ee0a50a751893913e2d3885
View on Chainz β†—

Difficulty

11.242934

Transactions

2

Size

1021 B

Version

2

Bits

0b3e30ec

Nonce

1,448,188,745

Timestamp

4/28/2018, 9:14:20 PM

Confirmations

4,196,192

Merkle Root

d145c86e756026a80de40e9f4d57df33a67c016b9c766ea59c6abc5759cbcd54
Transactions (2)
Coinbase4144df4c632748…913a6b9b0faebc
1 in β†’ 1 out7.9100 XPM110 B
AVNEXDRh…RPaQM1DE
7ad95730dd6cc1…6073b53b598c6c
5 in β†’ 2 out78.4725 XPM821 B
AHYE6ke5…BdPuZJKoAWT89jPj…72oMaMvX
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.

1.889 Γ— 10⁹⁴(95-digit number)
18890558479456175230…09994921522906543040
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
1.889 Γ— 10⁹⁴(95-digit number)
18890558479456175230…09994921522906543039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.889 Γ— 10⁹⁴(95-digit number)
18890558479456175230…09994921522906543041
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
3.778 Γ— 10⁹⁴(95-digit number)
37781116958912350461…19989843045813086079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.778 Γ— 10⁹⁴(95-digit number)
37781116958912350461…19989843045813086081
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
7.556 Γ— 10⁹⁴(95-digit number)
75562233917824700923…39979686091626172159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.556 Γ— 10⁹⁴(95-digit number)
75562233917824700923…39979686091626172161
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
1.511 Γ— 10⁹⁡(96-digit number)
15112446783564940184…79959372183252344319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.511 Γ— 10⁹⁡(96-digit number)
15112446783564940184…79959372183252344321
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
3.022 Γ— 10⁹⁡(96-digit number)
30224893567129880369…59918744366504688639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.022 Γ— 10⁹⁡(96-digit number)
30224893567129880369…59918744366504688641
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
6.044 Γ— 10⁹⁡(96-digit number)
60449787134259760738…19837488733009377279
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 2634397

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 25871d87ba1cad6b470367876376d10fead74c978ee0a50a751893913e2d3885

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 #2,634,397 on Chainz β†—
Circulating Supply:57,888,843 XPMΒ·at block #6,830,588 Β· updates every 60s
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