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Home/Chain Registry/Block #2,778,278

Block #2,778,278

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2018, 3:31:28 AM Β· Difficulty 11.6506 Β· 4,064,448 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e2090a2a6f1d954d192e7ac41105357a892edff64cc4aa2448bf392266e537f3
View on Chainz β†—

Difficulty

11.650632

Transactions

2

Size

724 B

Version

2

Bits

0ba68fca

Nonce

604,278,906

Timestamp

8/4/2018, 3:31:28 AM

Confirmations

4,064,448

Merkle Root

ec32c533330adda38720c708b154ebc5f20283e9a14b01346a6377c945baafab
Transactions (2)
Coinbaseeaf2c5cad38fe9…6ecf1dcde150a4
1 in β†’ 1 out7.3600 XPM110 B
AZtxQr2F…7grUWrUz
5408ddb6585c60…4a5e12ce9901c1
3 in β†’ 2 out76.9491 XPM523 B
AL9kW13U…5VGoKsRxAUVx4f64…3dGkdFch
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.

1.118 Γ— 10⁹⁸(99-digit number)
11186280617488985644…27565877405216808960
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
1.118 Γ— 10⁹⁸(99-digit number)
11186280617488985644…27565877405216808959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.118 Γ— 10⁹⁸(99-digit number)
11186280617488985644…27565877405216808961
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
2.237 Γ— 10⁹⁸(99-digit number)
22372561234977971289…55131754810433617919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.237 Γ— 10⁹⁸(99-digit number)
22372561234977971289…55131754810433617921
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
4.474 Γ— 10⁹⁸(99-digit number)
44745122469955942578…10263509620867235839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.474 Γ— 10⁹⁸(99-digit number)
44745122469955942578…10263509620867235841
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
8.949 Γ— 10⁹⁸(99-digit number)
89490244939911885157…20527019241734471679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.949 Γ— 10⁹⁸(99-digit number)
89490244939911885157…20527019241734471681
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
1.789 Γ— 10⁹⁹(100-digit number)
17898048987982377031…41054038483468943359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.789 Γ— 10⁹⁹(100-digit number)
17898048987982377031…41054038483468943361
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
3.579 Γ— 10⁹⁹(100-digit number)
35796097975964754062…82108076966937886719
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 2778278

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 e2090a2a6f1d954d192e7ac41105357a892edff64cc4aa2448bf392266e537f3

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 #2,778,278 on Chainz β†—
Circulating Supply:57,986,147 XPMΒ·at block #6,842,725 Β· updates every 60s
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