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Home/Chain Registry/Block #2,127,671

Block #2,127,671

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/22/2017, 4:15:01 AM Β· Difficulty 10.9179 Β· 4,704,357 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7929dbe339a1884a3c16ed2b145f9249cb74d24cc9fee2288bbfec00623f3169
View on Chainz β†—

Difficulty

10.917905

Transactions

1

Size

199 B

Version

2

Bits

0aeafbcd

Nonce

448,327,561

Timestamp

5/22/2017, 4:15:01 AM

Confirmations

4,704,357

Merkle Root

f617cf89f29acb46344982f23723ed6c1136c6ad6e56c7ba140b7914c5f36b4c
Transactions (1)
Coinbasef617cf89f29acb…0b7914c5f36b4c
1 in β†’ 1 out8.3800 XPM109 B
Ab6yLj7m…ciiJQ4sd
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.

4.103 Γ— 10⁹⁡(96-digit number)
41037798347423117811…41962352812709180800
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
4.103 Γ— 10⁹⁡(96-digit number)
41037798347423117811…41962352812709180799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.103 Γ— 10⁹⁡(96-digit number)
41037798347423117811…41962352812709180801
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
8.207 Γ— 10⁹⁡(96-digit number)
82075596694846235623…83924705625418361599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
8.207 Γ— 10⁹⁡(96-digit number)
82075596694846235623…83924705625418361601
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
1.641 Γ— 10⁹⁢(97-digit number)
16415119338969247124…67849411250836723199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.641 Γ— 10⁹⁢(97-digit number)
16415119338969247124…67849411250836723201
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
3.283 Γ— 10⁹⁢(97-digit number)
32830238677938494249…35698822501673446399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.283 Γ— 10⁹⁢(97-digit number)
32830238677938494249…35698822501673446401
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
6.566 Γ— 10⁹⁢(97-digit number)
65660477355876988499…71397645003346892799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.566 Γ— 10⁹⁢(97-digit number)
65660477355876988499…71397645003346892801
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
1.313 Γ— 10⁹⁷(98-digit number)
13132095471175397699…42795290006693785599
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 2127671

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 7929dbe339a1884a3c16ed2b145f9249cb74d24cc9fee2288bbfec00623f3169

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 #2,127,671 on Chainz β†—
Circulating Supply:57,900,355 XPMΒ·at block #6,832,027 Β· updates every 60s
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