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Home/Chain Registry/Block #2,812,804

Block #2,812,804

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 8/27/2018, 9:37:58 PM Β· Difficulty 11.6733 Β· 4,019,880 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
275d98f28d4aa5f011353eee3f8d7f45c01007b6f14031a07a1ca16f394cbfcc
View on Chainz β†—

Difficulty

11.673252

Transactions

2

Size

723 B

Version

2

Bits

0bac5a38

Nonce

659,611,863

Timestamp

8/27/2018, 9:37:58 PM

Confirmations

4,019,880

Merkle Root

c3bb43cbf8443aaa21dbcbc650a6361f62572e2f70e4887c333bd018295dc56a
Transactions (2)
Coinbase0fa42cfcb99c9e…a2c69c73ec03ce
1 in β†’ 1 out7.3400 XPM109 B
AJ2aPZNz…VJn7PHYD
c874b4a2665634…492cc6801b5187
3 in β†’ 2 out16.0121 XPM522 B
AcW2kyDw…v2zaUR1RAVWk1Am4…8fFrwK5Z
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.

6.629 Γ— 10⁹⁸(99-digit number)
66292030574979305346…76190483630213038080
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
6.629 Γ— 10⁹⁸(99-digit number)
66292030574979305346…76190483630213038079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.629 Γ— 10⁹⁸(99-digit number)
66292030574979305346…76190483630213038081
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
1.325 Γ— 10⁹⁹(100-digit number)
13258406114995861069…52380967260426076159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.325 Γ— 10⁹⁹(100-digit number)
13258406114995861069…52380967260426076161
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
2.651 Γ— 10⁹⁹(100-digit number)
26516812229991722138…04761934520852152319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.651 Γ— 10⁹⁹(100-digit number)
26516812229991722138…04761934520852152321
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
5.303 Γ— 10⁹⁹(100-digit number)
53033624459983444276…09523869041704304639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.303 Γ— 10⁹⁹(100-digit number)
53033624459983444276…09523869041704304641
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
1.060 Γ— 10¹⁰⁰(101-digit number)
10606724891996688855…19047738083408609279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.060 Γ— 10¹⁰⁰(101-digit number)
10606724891996688855…19047738083408609281
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
2.121 Γ— 10¹⁰⁰(101-digit number)
21213449783993377710…38095476166817218559
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 2812804

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 275d98f28d4aa5f011353eee3f8d7f45c01007b6f14031a07a1ca16f394cbfcc

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 #2,812,804 on Chainz β†—
Circulating Supply:57,905,627 XPMΒ·at block #6,832,683 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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