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Home/Chain Registry/Block #2,177,867

Block #2,177,867

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/25/2017, 7:20:25 PM Β· Difficulty 10.9243 Β· 4,654,532 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dcb978fa0ba7d074d36d9b3276595c71869475b5be26569bf2d018c866d8081b
View on Chainz β†—

Difficulty

10.924293

Transactions

1

Size

199 B

Version

2

Bits

0aec9e7e

Nonce

1,056,343,545

Timestamp

6/25/2017, 7:20:25 PM

Confirmations

4,654,532

Merkle Root

e93983911d1033ca605df81added1f51961bdda34a98e627a6e5db811b1509c1
Transactions (1)
Coinbasee93983911d1033…e5db811b1509c1
1 in β†’ 1 out8.3700 XPM109 B
Aeyfcpvd…c2qbpf9Z
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.

7.354 Γ— 10⁹³(94-digit number)
73540866688111045244…52158367432201295040
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
7.354 Γ— 10⁹³(94-digit number)
73540866688111045244…52158367432201295039
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.354 Γ— 10⁹³(94-digit number)
73540866688111045244…52158367432201295041
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
1.470 Γ— 10⁹⁴(95-digit number)
14708173337622209048…04316734864402590079
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.470 Γ— 10⁹⁴(95-digit number)
14708173337622209048…04316734864402590081
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
2.941 Γ— 10⁹⁴(95-digit number)
29416346675244418097…08633469728805180159
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.941 Γ— 10⁹⁴(95-digit number)
29416346675244418097…08633469728805180161
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
5.883 Γ— 10⁹⁴(95-digit number)
58832693350488836195…17266939457610360319
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.883 Γ— 10⁹⁴(95-digit number)
58832693350488836195…17266939457610360321
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
1.176 Γ— 10⁹⁡(96-digit number)
11766538670097767239…34533878915220720639
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.176 Γ— 10⁹⁡(96-digit number)
11766538670097767239…34533878915220720641
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 2177867

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 dcb978fa0ba7d074d36d9b3276595c71869475b5be26569bf2d018c866d8081b

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 #2,177,867 on Chainz β†—
Circulating Supply:57,903,335 XPMΒ·at block #6,832,398 Β· updates every 60s
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