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Home/Chain Registry/Block #1,687,460

Block #1,687,460

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/24/2016, 3:07:12 PM Β· Difficulty 10.7083 Β· 5,143,393 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
0efce774fdbffd4a81e7c61dc54c8a46cf9f5266adea32311ccc1fe99a56c148
View on Chainz β†—

Difficulty

10.708266

Transactions

1

Size

201 B

Version

2

Bits

0ab550ee

Nonce

1,295,607,406

Timestamp

7/24/2016, 3:07:12 PM

Confirmations

5,143,393

Merkle Root

b4b10f1795ac81afa6fe1f145253e62c600debfbc9f635dc21f344a2787a9030
Transactions (1)
Coinbaseb4b10f1795ac81…f344a2787a9030
1 in β†’ 1 out8.7100 XPM110 B
AVVexHBM…uF4WLYgz
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.

8.113 Γ— 10⁹⁢(97-digit number)
81138688209832219023…71903770301699133440
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
8.113 Γ— 10⁹⁢(97-digit number)
81138688209832219023…71903770301699133439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.113 Γ— 10⁹⁢(97-digit number)
81138688209832219023…71903770301699133441
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
1.622 Γ— 10⁹⁷(98-digit number)
16227737641966443804…43807540603398266879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.622 Γ— 10⁹⁷(98-digit number)
16227737641966443804…43807540603398266881
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
3.245 Γ— 10⁹⁷(98-digit number)
32455475283932887609…87615081206796533759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.245 Γ— 10⁹⁷(98-digit number)
32455475283932887609…87615081206796533761
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
6.491 Γ— 10⁹⁷(98-digit number)
64910950567865775218…75230162413593067519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.491 Γ— 10⁹⁷(98-digit number)
64910950567865775218…75230162413593067521
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
1.298 Γ— 10⁹⁸(99-digit number)
12982190113573155043…50460324827186135039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.298 Γ— 10⁹⁸(99-digit number)
12982190113573155043…50460324827186135041
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 1687460

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 0efce774fdbffd4a81e7c61dc54c8a46cf9f5266adea32311ccc1fe99a56c148

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 #1,687,460 on Chainz β†—
Circulating Supply:57,890,959 XPMΒ·at block #6,830,852 Β· updates every 60s
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