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Home/Chain Registry/Block #2,281,777

Block #2,281,777

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 9/4/2017, 7:40:42 AM Β· Difficulty 10.9555 Β· 4,550,011 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2eb0e94383d5e1731bb850a95ee82b6077cdb021168f1517340dc28e0107f7e6
View on Chainz β†—

Difficulty

10.955504

Transactions

1

Size

199 B

Version

2

Bits

0af49be4

Nonce

699,858,805

Timestamp

9/4/2017, 7:40:42 AM

Confirmations

4,550,011

Merkle Root

c945a248476de3acc873b97007d273f2de2d691885aa7297e675f02090c3b69c
Transactions (1)
Coinbasec945a248476de3…75f02090c3b69c
1 in β†’ 1 out8.3200 XPM109 B
AeCCv3kL…PB4DgFoS
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.

6.882 Γ— 10⁹³(94-digit number)
68826389661507320688…10366068888571077120
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
6.882 Γ— 10⁹³(94-digit number)
68826389661507320688…10366068888571077119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.882 Γ— 10⁹³(94-digit number)
68826389661507320688…10366068888571077121
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
1.376 Γ— 10⁹⁴(95-digit number)
13765277932301464137…20732137777142154239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.376 Γ— 10⁹⁴(95-digit number)
13765277932301464137…20732137777142154241
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
2.753 Γ— 10⁹⁴(95-digit number)
27530555864602928275…41464275554284308479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.753 Γ— 10⁹⁴(95-digit number)
27530555864602928275…41464275554284308481
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
5.506 Γ— 10⁹⁴(95-digit number)
55061111729205856551…82928551108568616959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.506 Γ— 10⁹⁴(95-digit number)
55061111729205856551…82928551108568616961
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
1.101 Γ— 10⁹⁡(96-digit number)
11012222345841171310…65857102217137233919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.101 Γ— 10⁹⁡(96-digit number)
11012222345841171310…65857102217137233921
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
2.202 Γ— 10⁹⁡(96-digit number)
22024444691682342620…31714204434274467839
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 2281777

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 2eb0e94383d5e1731bb850a95ee82b6077cdb021168f1517340dc28e0107f7e6

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 #2,281,777 on Chainz β†—
Circulating Supply:57,898,418 XPMΒ·at block #6,831,787 Β· updates every 60s
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