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Home/Chain Registry/Block #2,175,302

Block #2,175,302

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/24/2017, 10:23:22 AM Β· Difficulty 10.9148 Β· 4,666,371 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
ec971f8bce935eb2d2b825bfb5b829c20ae4ce2c8d287bd70698ee8643bf0072
View on Chainz β†—

Difficulty

10.914846

Transactions

1

Size

200 B

Version

2

Bits

0aea3353

Nonce

736,915,165

Timestamp

6/24/2017, 10:23:22 AM

Confirmations

4,666,371

Merkle Root

8753d72a5e39899e5a633eea8afe4a043adfce670091224495ec4efe3804aea1
Transactions (1)
Coinbase8753d72a5e3989…ec4efe3804aea1
1 in β†’ 1 out8.3800 XPM109 B
AKeoBnmw…ryGkLB9k
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.

7.659 Γ— 10⁹⁢(97-digit number)
76598733040981008946…99772705738294968320
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
7.659 Γ— 10⁹⁢(97-digit number)
76598733040981008946…99772705738294968319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.659 Γ— 10⁹⁢(97-digit number)
76598733040981008946…99772705738294968321
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
1.531 Γ— 10⁹⁷(98-digit number)
15319746608196201789…99545411476589936639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.531 Γ— 10⁹⁷(98-digit number)
15319746608196201789…99545411476589936641
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
3.063 Γ— 10⁹⁷(98-digit number)
30639493216392403578…99090822953179873279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.063 Γ— 10⁹⁷(98-digit number)
30639493216392403578…99090822953179873281
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
6.127 Γ— 10⁹⁷(98-digit number)
61278986432784807157…98181645906359746559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.127 Γ— 10⁹⁷(98-digit number)
61278986432784807157…98181645906359746561
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
1.225 Γ— 10⁹⁸(99-digit number)
12255797286556961431…96363291812719493119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.225 Γ— 10⁹⁸(99-digit number)
12255797286556961431…96363291812719493121
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
2.451 Γ— 10⁹⁸(99-digit number)
24511594573113922862…92726583625438986239
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 2175302

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 ec971f8bce935eb2d2b825bfb5b829c20ae4ce2c8d287bd70698ee8643bf0072

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 #2,175,302 on Chainz β†—
Circulating Supply:57,977,771 XPMΒ·at block #6,841,672 Β· updates every 60s
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