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Home/Chain Registry/Block #2,647,367

Block #2,647,367

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/3/2018, 9:34:31 PM Β· Difficulty 11.7583 Β· 4,192,060 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ce8cda0c067fab2c6c4e41ef5126552386a5b5e4a52da4acc34eacc6a6db4089
View on Chainz β†—

Difficulty

11.758321

Transactions

1

Size

200 B

Version

2

Bits

0bc22155

Nonce

136,950,451

Timestamp

5/3/2018, 9:34:31 PM

Confirmations

4,192,060

Merkle Root

287c2cffb403a4d03e282b7141f3b27a2827d970dd36b50c831dcdf57a678777
Transactions (1)
Coinbase287c2cffb403a4…1dcdf57a678777
1 in β†’ 1 out7.2200 XPM110 B
AeNgXkkj…44fftCNN
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.

5.541 Γ— 10⁹³(94-digit number)
55414229100018298726…02393443532047621060
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
5.541 Γ— 10⁹³(94-digit number)
55414229100018298726…02393443532047621059
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.541 Γ— 10⁹³(94-digit number)
55414229100018298726…02393443532047621061
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
1.108 Γ— 10⁹⁴(95-digit number)
11082845820003659745…04786887064095242119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.108 Γ— 10⁹⁴(95-digit number)
11082845820003659745…04786887064095242121
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
2.216 Γ— 10⁹⁴(95-digit number)
22165691640007319490…09573774128190484239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.216 Γ— 10⁹⁴(95-digit number)
22165691640007319490…09573774128190484241
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
4.433 Γ— 10⁹⁴(95-digit number)
44331383280014638981…19147548256380968479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.433 Γ— 10⁹⁴(95-digit number)
44331383280014638981…19147548256380968481
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
8.866 Γ— 10⁹⁴(95-digit number)
88662766560029277962…38295096512761936959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.866 Γ— 10⁹⁴(95-digit number)
88662766560029277962…38295096512761936961
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
1.773 Γ— 10⁹⁡(96-digit number)
17732553312005855592…76590193025523873919
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 2647367

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 ce8cda0c067fab2c6c4e41ef5126552386a5b5e4a52da4acc34eacc6a6db4089

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 #2,647,367 on Chainz β†—
Circulating Supply:57,959,705 XPMΒ·at block #6,839,426 Β· updates every 60s
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