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Home/Chain Registry/Block #2,139,005

Block #2,139,005

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/31/2017, 9:11:55 AM Β· Difficulty 10.8802 Β· 4,703,874 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
638e4939079ea92849208dc499be12df9507f947433eafaf7bc7a10b38fbdcf8
View on Chainz β†—

Difficulty

10.880175

Transactions

1

Size

198 B

Version

2

Bits

0ae1531f

Nonce

646,051,418

Timestamp

5/31/2017, 9:11:55 AM

Confirmations

4,703,874

Merkle Root

040bef38636ad235216dda8ef742ca158d17b32e2713ac9c1a45973f5a42a06d
Transactions (1)
Coinbase040bef38636ad2…45973f5a42a06d
1 in β†’ 1 out8.4300 XPM109 B
APdfHbqq…6YiBuW5U
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.

1.354 Γ— 10⁹³(94-digit number)
13542712674455989582…59763884078715543840
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
1.354 Γ— 10⁹³(94-digit number)
13542712674455989582…59763884078715543839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.354 Γ— 10⁹³(94-digit number)
13542712674455989582…59763884078715543841
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
2.708 Γ— 10⁹³(94-digit number)
27085425348911979164…19527768157431087679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.708 Γ— 10⁹³(94-digit number)
27085425348911979164…19527768157431087681
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
5.417 Γ— 10⁹³(94-digit number)
54170850697823958328…39055536314862175359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.417 Γ— 10⁹³(94-digit number)
54170850697823958328…39055536314862175361
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
1.083 Γ— 10⁹⁴(95-digit number)
10834170139564791665…78111072629724350719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.083 Γ— 10⁹⁴(95-digit number)
10834170139564791665…78111072629724350721
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
2.166 Γ— 10⁹⁴(95-digit number)
21668340279129583331…56222145259448701439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.166 Γ— 10⁹⁴(95-digit number)
21668340279129583331…56222145259448701441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 2139005

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 638e4939079ea92849208dc499be12df9507f947433eafaf7bc7a10b38fbdcf8

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 #2,139,005 on Chainz β†—
Circulating Supply:57,987,376 XPMΒ·at block #6,842,878 Β· updates every 60s
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