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Home/Chain Registry/Block #2,756,537

Block #2,756,537

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/19/2018, 9:17:44 PM Β· Difficulty 11.6656 Β· 4,080,132 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2111afde786ba666a5c6e5e09fac477a3ac408dfffe2e2feb79f2f8be299ecce
View on Chainz β†—

Difficulty

11.665557

Transactions

1

Size

200 B

Version

2

Bits

0baa61f0

Nonce

500,845,305

Timestamp

7/19/2018, 9:17:44 PM

Confirmations

4,080,132

Merkle Root

5726112e8c04f948f8c8bf965ddde9a55836c709d9e8af4494385a132097b0b2
Transactions (1)
Coinbase5726112e8c04f9…385a132097b0b2
1 in β†’ 1 out7.3400 XPM110 B
AQuYtLfg…dGfJJxaW
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.

1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149600
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
1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.159 Γ— 10⁹⁡(96-digit number)
11592025167819203999…14073974658870149601
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
2.318 Γ— 10⁹⁡(96-digit number)
23184050335638407998…28147949317740299199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.318 Γ— 10⁹⁡(96-digit number)
23184050335638407998…28147949317740299201
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
4.636 Γ— 10⁹⁡(96-digit number)
46368100671276815997…56295898635480598399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.636 Γ— 10⁹⁡(96-digit number)
46368100671276815997…56295898635480598401
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
9.273 Γ— 10⁹⁡(96-digit number)
92736201342553631994…12591797270961196799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.273 Γ— 10⁹⁡(96-digit number)
92736201342553631994…12591797270961196801
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
1.854 Γ— 10⁹⁢(97-digit number)
18547240268510726398…25183594541922393599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.854 Γ— 10⁹⁢(97-digit number)
18547240268510726398…25183594541922393601
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
3.709 Γ— 10⁹⁢(97-digit number)
37094480537021452797…50367189083844787199
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 2756537

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 2111afde786ba666a5c6e5e09fac477a3ac408dfffe2e2feb79f2f8be299ecce

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 #2,756,537 on Chainz β†—
Circulating Supply:57,937,630 XPMΒ·at block #6,836,668 Β· updates every 60s
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