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Home/Chain Registry/Block #2,176,614

Block #2,176,614

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 2:41:33 AM Β· Difficulty 10.9203 Β· 4,650,364 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
78b1396f04c30f7ae8356656985d6c13dd6640bbbe90fd171e0a8887f4ba4f6a
View on Chainz β†—

Difficulty

10.920346

Transactions

1

Size

200 B

Version

2

Bits

0aeb9bc6

Nonce

1,244,722,437

Timestamp

6/25/2017, 2:41:33 AM

Confirmations

4,650,364

Merkle Root

5d5274b09fd002930b3f265d6555bfb0e7c76cd3b8a35f30899b799504a13687
Transactions (1)
Coinbase5d5274b09fd002…9b799504a13687
1 in β†’ 1 out8.3700 XPM110 B
AWszGVnc…SRmWMCdK
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.

7.692 Γ— 10⁹³(94-digit number)
76927855158847605306…49193631482147471360
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
7.692 Γ— 10⁹³(94-digit number)
76927855158847605306…49193631482147471359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.692 Γ— 10⁹³(94-digit number)
76927855158847605306…49193631482147471361
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
1.538 Γ— 10⁹⁴(95-digit number)
15385571031769521061…98387262964294942719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.538 Γ— 10⁹⁴(95-digit number)
15385571031769521061…98387262964294942721
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
3.077 Γ— 10⁹⁴(95-digit number)
30771142063539042122…96774525928589885439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.077 Γ— 10⁹⁴(95-digit number)
30771142063539042122…96774525928589885441
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
6.154 Γ— 10⁹⁴(95-digit number)
61542284127078084244…93549051857179770879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.154 Γ— 10⁹⁴(95-digit number)
61542284127078084244…93549051857179770881
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
1.230 Γ— 10⁹⁡(96-digit number)
12308456825415616848…87098103714359541759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.230 Γ— 10⁹⁡(96-digit number)
12308456825415616848…87098103714359541761
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 2176614

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 78b1396f04c30f7ae8356656985d6c13dd6640bbbe90fd171e0a8887f4ba4f6a

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 #2,176,614 on Chainz β†—
Circulating Supply:57,859,998 XPMΒ·at block #6,826,977 Β· updates every 60s
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