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Home/Chain Registry/Block #2,147,697

Block #2,147,697

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/6/2017, 12:01:00 AM Β· Difficulty 10.8939 Β· 4,688,822 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ba2522ccc703e5f8f6319e0c5414eacd2bf859d9e2ea759f5ad9bc064d97de4e
View on Chainz β†—

Difficulty

10.893920

Transactions

1

Size

208 B

Version

2

Bits

0ae4d7f3

Nonce

124,784,627

Timestamp

6/6/2017, 12:01:00 AM

Confirmations

4,688,822

Merkle Root

a862d7649f72b3f7e11eeafe8eccd9aef9104810ce5332287d07d8c7c89ac851
Transactions (1)
Coinbasea862d7649f72b3…07d8c7c89ac851
1 in β†’ 1 out8.4100 XPM118 B
AM6GYpjw…aw86QDtR
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.

1.502 Γ— 10⁹⁡(96-digit number)
15028087858179415187…29728343803117779000
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
1.502 Γ— 10⁹⁡(96-digit number)
15028087858179415187…29728343803117778999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.502 Γ— 10⁹⁡(96-digit number)
15028087858179415187…29728343803117779001
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
3.005 Γ— 10⁹⁡(96-digit number)
30056175716358830374…59456687606235557999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.005 Γ— 10⁹⁡(96-digit number)
30056175716358830374…59456687606235558001
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
6.011 Γ— 10⁹⁡(96-digit number)
60112351432717660748…18913375212471115999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.011 Γ— 10⁹⁡(96-digit number)
60112351432717660748…18913375212471116001
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
1.202 Γ— 10⁹⁢(97-digit number)
12022470286543532149…37826750424942231999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.202 Γ— 10⁹⁢(97-digit number)
12022470286543532149…37826750424942232001
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
2.404 Γ— 10⁹⁢(97-digit number)
24044940573087064299…75653500849884463999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.404 Γ— 10⁹⁢(97-digit number)
24044940573087064299…75653500849884464001
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
4.808 Γ— 10⁹⁢(97-digit number)
48089881146174128598…51307001699768927999
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 2147697

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 ba2522ccc703e5f8f6319e0c5414eacd2bf859d9e2ea759f5ad9bc064d97de4e

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 #2,147,697 on Chainz β†—
Circulating Supply:57,936,429 XPMΒ·at block #6,836,518 Β· updates every 60s
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