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Home/Chain Registry/Block #2,177,917

Block #2,177,917

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:51:57 PM Β· Difficulty 10.9246 Β· 4,652,847 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
54654669acab2801d1eda3d39e8559a0aa3923477c18896398acd5364212cd66
View on Chainz β†—

Difficulty

10.924565

Transactions

1

Size

200 B

Version

2

Bits

0aecb046

Nonce

872,077,907

Timestamp

6/25/2017, 7:51:57 PM

Confirmations

4,652,847

Merkle Root

91e8e5821e791784e8d0ec658503e4a4b72ee9c7809f560ffb3c90f0d6092ac7
Transactions (1)
Coinbase91e8e5821e7917…3c90f0d6092ac7
1 in β†’ 1 out8.3700 XPM110 B
AXX7BNZt…UbPqqM5Q
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.

1.020 Γ— 10⁹⁡(96-digit number)
10207944239657692018…25630088530708054400
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
1.020 Γ— 10⁹⁡(96-digit number)
10207944239657692018…25630088530708054399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.020 Γ— 10⁹⁡(96-digit number)
10207944239657692018…25630088530708054401
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
2.041 Γ— 10⁹⁡(96-digit number)
20415888479315384036…51260177061416108799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.041 Γ— 10⁹⁡(96-digit number)
20415888479315384036…51260177061416108801
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
4.083 Γ— 10⁹⁡(96-digit number)
40831776958630768073…02520354122832217599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.083 Γ— 10⁹⁡(96-digit number)
40831776958630768073…02520354122832217601
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
8.166 Γ— 10⁹⁡(96-digit number)
81663553917261536146…05040708245664435199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.166 Γ— 10⁹⁡(96-digit number)
81663553917261536146…05040708245664435201
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
1.633 Γ— 10⁹⁢(97-digit number)
16332710783452307229…10081416491328870399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.633 Γ— 10⁹⁢(97-digit number)
16332710783452307229…10081416491328870401
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 2177917

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 54654669acab2801d1eda3d39e8559a0aa3923477c18896398acd5364212cd66

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 #2,177,917 on Chainz β†—
Circulating Supply:57,890,248 XPMΒ·at block #6,830,763 Β· updates every 60s
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