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Home/Chain Registry/Block #2,634,356

Block #2,634,356

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/28/2018, 8:51:01 PM Β· Difficulty 11.2401 Β· 4,202,187 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d1527613f2fddfba35f6595345fa03582454543d9d32c419eae65e7484d3703f
View on Chainz β†—

Difficulty

11.240126

Transactions

1

Size

199 B

Version

2

Bits

0b3d78e4

Nonce

1,670,907,253

Timestamp

4/28/2018, 8:51:01 PM

Confirmations

4,202,187

Merkle Root

ba4f8612c4ab3e38124738db0f966109c42a90d77d31ff97f4f831aad38e76e2
Transactions (1)
Coinbaseba4f8612c4ab3e…f831aad38e76e2
1 in β†’ 1 out7.9000 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.

1.594 Γ— 10⁹⁴(95-digit number)
15944077013129376737…97721596450103551100
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
1.594 Γ— 10⁹⁴(95-digit number)
15944077013129376737…97721596450103551099
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.594 Γ— 10⁹⁴(95-digit number)
15944077013129376737…97721596450103551101
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
3.188 Γ— 10⁹⁴(95-digit number)
31888154026258753475…95443192900207102199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.188 Γ— 10⁹⁴(95-digit number)
31888154026258753475…95443192900207102201
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
6.377 Γ— 10⁹⁴(95-digit number)
63776308052517506951…90886385800414204399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.377 Γ— 10⁹⁴(95-digit number)
63776308052517506951…90886385800414204401
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
1.275 Γ— 10⁹⁡(96-digit number)
12755261610503501390…81772771600828408799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.275 Γ— 10⁹⁡(96-digit number)
12755261610503501390…81772771600828408801
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
2.551 Γ— 10⁹⁡(96-digit number)
25510523221007002780…63545543201656817599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.551 Γ— 10⁹⁡(96-digit number)
25510523221007002780…63545543201656817601
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
5.102 Γ— 10⁹⁡(96-digit number)
51021046442014005561…27091086403313635199
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 2634356

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 d1527613f2fddfba35f6595345fa03582454543d9d32c419eae65e7484d3703f

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 #2,634,356 on Chainz β†—
Circulating Supply:57,936,609 XPMΒ·at block #6,836,542 Β· updates every 60s
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