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Home/Chain Registry/Block #1,647,132

Block #1,647,132

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/27/2016, 4:04:00 AM Β· Difficulty 10.6571 Β· 5,177,554 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
41931fba09c0f82082e6b60eb18d20fd1174fdc11ee8c93198fdb8a1945fa4ff
View on Chainz β†—

Difficulty

10.657138

Transactions

1

Size

198 B

Version

2

Bits

0aa83a3a

Nonce

1,685,502,109

Timestamp

6/27/2016, 4:04:00 AM

Confirmations

5,177,554

Merkle Root

d152a01c8af505aada9bf83fc416ebb594bbf0a531d3babd56283aed8f1be87b
Transactions (1)
Coinbased152a01c8af505…283aed8f1be87b
1 in β†’ 1 out8.7900 XPM109 B
AdkzFmCZ…qk7jFYnn
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.

6.402 Γ— 10⁹²(93-digit number)
64021225530301377630…12189117343695953440
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
6.402 Γ— 10⁹²(93-digit number)
64021225530301377630…12189117343695953439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.402 Γ— 10⁹²(93-digit number)
64021225530301377630…12189117343695953441
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
1.280 Γ— 10⁹³(94-digit number)
12804245106060275526…24378234687391906879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.280 Γ— 10⁹³(94-digit number)
12804245106060275526…24378234687391906881
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
2.560 Γ— 10⁹³(94-digit number)
25608490212120551052…48756469374783813759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.560 Γ— 10⁹³(94-digit number)
25608490212120551052…48756469374783813761
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
5.121 Γ— 10⁹³(94-digit number)
51216980424241102104…97512938749567627519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.121 Γ— 10⁹³(94-digit number)
51216980424241102104…97512938749567627521
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
1.024 Γ— 10⁹⁴(95-digit number)
10243396084848220420…95025877499135255039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.024 Γ— 10⁹⁴(95-digit number)
10243396084848220420…95025877499135255041
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 1647132

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 41931fba09c0f82082e6b60eb18d20fd1174fdc11ee8c93198fdb8a1945fa4ff

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 #1,647,132 on Chainz β†—
Circulating Supply:57,841,554 XPMΒ·at block #6,824,685 Β· updates every 60s
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