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Home/Chain Registry/Block #2,138,140

Block #2,138,140

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 5/30/2017, 3:20:53 PM Β· Difficulty 10.8850 Β· 4,704,841 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8402e694efffd4007ea7d95135a7a459a1292ff5aee6a0b5b4e64e6086a95d04
View on Chainz β†—

Difficulty

10.885006

Transactions

2

Size

1.54 KB

Version

2

Bits

0ae28fc1

Nonce

2,063,497,400

Timestamp

5/30/2017, 3:20:53 PM

Confirmations

4,704,841

Merkle Root

d4fa4336466a96cf04fe28c3be9ecaab5b5761190f8590764efb5a0bd18171c7
Transactions (2)
Coinbase8f42e8449c7e3e…ba2281bf7df62f
1 in β†’ 1 out8.4600 XPM110 B
Ab26e7ef…UrLPfJkg
5bbdf09a5b158f…759c425512afc5
9 in β†’ 1 out2220.9605 XPM1.34 KB
AKJGQErc…h7EKNrfs
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.

1.655 Γ— 10⁹⁸(99-digit number)
16556629116926139392…73395836860069068800
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
1.655 Γ— 10⁹⁸(99-digit number)
16556629116926139392…73395836860069068799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.655 Γ— 10⁹⁸(99-digit number)
16556629116926139392…73395836860069068801
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
3.311 Γ— 10⁹⁸(99-digit number)
33113258233852278785…46791673720138137599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.311 Γ— 10⁹⁸(99-digit number)
33113258233852278785…46791673720138137601
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
6.622 Γ— 10⁹⁸(99-digit number)
66226516467704557571…93583347440276275199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.622 Γ— 10⁹⁸(99-digit number)
66226516467704557571…93583347440276275201
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
1.324 Γ— 10⁹⁹(100-digit number)
13245303293540911514…87166694880552550399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.324 Γ— 10⁹⁹(100-digit number)
13245303293540911514…87166694880552550401
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
2.649 Γ— 10⁹⁹(100-digit number)
26490606587081823028…74333389761105100799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.649 Γ— 10⁹⁹(100-digit number)
26490606587081823028…74333389761105100801
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 2138140

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 8402e694efffd4007ea7d95135a7a459a1292ff5aee6a0b5b4e64e6086a95d04

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 #2,138,140 on Chainz β†—
Circulating Supply:57,988,202 XPMΒ·at block #6,842,980 Β· updates every 60s
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