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Home/Chain Registry/Block #2,749,178

Block #2,749,178

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/14/2018, 11:04:54 PM Β· Difficulty 11.6472 Β· 4,084,436 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
95646885669d6b8090092b415708bf6ee0c8e0647621714bb9eba4d687e4f5a3
View on Chainz β†—

Difficulty

11.647225

Transactions

2

Size

426 B

Version

2

Bits

0ba5b087

Nonce

1,036,711,887

Timestamp

7/14/2018, 11:04:54 PM

Confirmations

4,084,436

Merkle Root

c6c719bac4bbb46e7ed656fb3610bf94e43bda697191e2d4b1241f9e36a5b304
Transactions (2)
Coinbase55ee8df7b17d6e…89d5978878f4c9
1 in β†’ 1 out7.3700 XPM109 B
AHPog2JU…tzDdcmmm
fdade042a3a18a…6f2baae80197f9
1 in β†’ 2 out0.9306 XPM226 B
Aa1cbLt5…Nf58QkZTAKSzwum5…o4LLQ4B1
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.

5.391 Γ— 10⁹⁷(98-digit number)
53916013852048280913…80972213891452303360
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
5.391 Γ— 10⁹⁷(98-digit number)
53916013852048280913…80972213891452303359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.391 Γ— 10⁹⁷(98-digit number)
53916013852048280913…80972213891452303361
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
1.078 Γ— 10⁹⁸(99-digit number)
10783202770409656182…61944427782904606719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.078 Γ— 10⁹⁸(99-digit number)
10783202770409656182…61944427782904606721
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
2.156 Γ— 10⁹⁸(99-digit number)
21566405540819312365…23888855565809213439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.156 Γ— 10⁹⁸(99-digit number)
21566405540819312365…23888855565809213441
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
4.313 Γ— 10⁹⁸(99-digit number)
43132811081638624730…47777711131618426879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.313 Γ— 10⁹⁸(99-digit number)
43132811081638624730…47777711131618426881
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
8.626 Γ— 10⁹⁸(99-digit number)
86265622163277249461…95555422263236853759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.626 Γ— 10⁹⁸(99-digit number)
86265622163277249461…95555422263236853761
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
1.725 Γ— 10⁹⁹(100-digit number)
17253124432655449892…91110844526473707519
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 2749178

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 95646885669d6b8090092b415708bf6ee0c8e0647621714bb9eba4d687e4f5a3

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 #2,749,178 on Chainz β†—
Circulating Supply:57,913,122 XPMΒ·at block #6,833,613 Β· updates every 60s
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