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Home/Chain Registry/Block #1,691,258

Block #1,691,258

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2016, 11:47:22 AM Β· Difficulty 10.6893 Β· 5,148,031 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
6064ebbd3d5a2ee6d13a74fc6cd7c3707e5711a4a76cd5808fcfc1e281954566
View on Chainz β†—

Difficulty

10.689334

Transactions

1

Size

198 B

Version

2

Bits

0ab07839

Nonce

586,435,491

Timestamp

7/27/2016, 11:47:22 AM

Confirmations

5,148,031

Merkle Root

309cd39c979e21f4036f5cd9495c992ecbb9450112005d24da23bd18d73b1dfe
Transactions (1)
Coinbase309cd39c979e21…23bd18d73b1dfe
1 in β†’ 1 out8.7400 XPM109 B
ANnXgBDw…uWYbrZvY
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.

1.271 Γ— 10⁹³(94-digit number)
12717966158847985458…47537580296940131800
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
1.271 Γ— 10⁹³(94-digit number)
12717966158847985458…47537580296940131799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.271 Γ— 10⁹³(94-digit number)
12717966158847985458…47537580296940131801
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
2.543 Γ— 10⁹³(94-digit number)
25435932317695970917…95075160593880263599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.543 Γ— 10⁹³(94-digit number)
25435932317695970917…95075160593880263601
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
5.087 Γ— 10⁹³(94-digit number)
50871864635391941834…90150321187760527199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.087 Γ— 10⁹³(94-digit number)
50871864635391941834…90150321187760527201
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
1.017 Γ— 10⁹⁴(95-digit number)
10174372927078388366…80300642375521054399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.017 Γ— 10⁹⁴(95-digit number)
10174372927078388366…80300642375521054401
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
2.034 Γ— 10⁹⁴(95-digit number)
20348745854156776733…60601284751042108799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.034 Γ— 10⁹⁴(95-digit number)
20348745854156776733…60601284751042108801
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
4.069 Γ— 10⁹⁴(95-digit number)
40697491708313553467…21202569502084217599
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 1691258

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 6064ebbd3d5a2ee6d13a74fc6cd7c3707e5711a4a76cd5808fcfc1e281954566

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 #1,691,258 on Chainz β†—
Circulating Supply:57,958,599 XPMΒ·at block #6,839,288 Β· updates every 60s
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