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Home/Chain Registry/Block #2,652,011

Block #2,652,011

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2018, 6:43:56 AM Β· Difficulty 11.7474 Β· 4,193,143 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a724aa39d30f7dab9a66f2b5fc98c6782208c3868a40454a4bcf1dc7a81a46bc
View on Chainz β†—

Difficulty

11.747395

Transactions

1

Size

200 B

Version

2

Bits

0bbf554e

Nonce

194,122,918

Timestamp

5/7/2018, 6:43:56 AM

Confirmations

4,193,143

Merkle Root

5371ea952d7e1952d1b3d81162721ac0437bc7ad469a05b978634f864e8ef362
Transactions (1)
Coinbase5371ea952d7e19…634f864e8ef362
1 in β†’ 1 out7.2300 XPM110 B
AMW7umb9…ofgZ6jMC
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.

8.442 Γ— 10⁹⁴(95-digit number)
84425753081390581989…34529659406183243200
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
8.442 Γ— 10⁹⁴(95-digit number)
84425753081390581989…34529659406183243199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.442 Γ— 10⁹⁴(95-digit number)
84425753081390581989…34529659406183243201
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
1.688 Γ— 10⁹⁡(96-digit number)
16885150616278116397…69059318812366486399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.688 Γ— 10⁹⁡(96-digit number)
16885150616278116397…69059318812366486401
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
3.377 Γ— 10⁹⁡(96-digit number)
33770301232556232795…38118637624732972799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.377 Γ— 10⁹⁡(96-digit number)
33770301232556232795…38118637624732972801
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
6.754 Γ— 10⁹⁡(96-digit number)
67540602465112465591…76237275249465945599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.754 Γ— 10⁹⁡(96-digit number)
67540602465112465591…76237275249465945601
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
1.350 Γ— 10⁹⁢(97-digit number)
13508120493022493118…52474550498931891199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.350 Γ— 10⁹⁢(97-digit number)
13508120493022493118…52474550498931891201
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
2.701 Γ— 10⁹⁢(97-digit number)
27016240986044986236…04949100997863782399
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 2652011

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 a724aa39d30f7dab9a66f2b5fc98c6782208c3868a40454a4bcf1dc7a81a46bc

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 #2,652,011 on Chainz β†—
Circulating Supply:58,005,660 XPMΒ·at block #6,845,153 Β· updates every 60s
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