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Home/Chain Registry/Block #2,921,880

Block #2,921,880

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/13/2018, 10:58:28 PM Β· Difficulty 11.3751 Β· 3,911,690 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
950c75c6a3463a98d7e1da2264c5e7e0347958f59422081aa9a7d69ddd7d136f
View on Chainz β†—

Difficulty

11.375147

Transactions

1

Size

199 B

Version

2

Bits

0b6009a0

Nonce

1,009,743,371

Timestamp

11/13/2018, 10:58:28 PM

Confirmations

3,911,690

Merkle Root

64f14dddff0555d9e1af4af3c4e2c1b0b27cb261353316b9a1d2d21e45e19a70
Transactions (1)
Coinbase64f14dddff0555…d2d21e45e19a70
1 in β†’ 1 out7.7200 XPM109 B
AUhjokok…k5m93PZR
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.

2.008 Γ— 10⁹⁴(95-digit number)
20089345192924854689…07238819546033920000
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
2.008 Γ— 10⁹⁴(95-digit number)
20089345192924854689…07238819546033919999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.008 Γ— 10⁹⁴(95-digit number)
20089345192924854689…07238819546033920001
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
4.017 Γ— 10⁹⁴(95-digit number)
40178690385849709378…14477639092067839999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.017 Γ— 10⁹⁴(95-digit number)
40178690385849709378…14477639092067840001
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
8.035 Γ— 10⁹⁴(95-digit number)
80357380771699418757…28955278184135679999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.035 Γ— 10⁹⁴(95-digit number)
80357380771699418757…28955278184135680001
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
1.607 Γ— 10⁹⁡(96-digit number)
16071476154339883751…57910556368271359999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.607 Γ— 10⁹⁡(96-digit number)
16071476154339883751…57910556368271360001
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
3.214 Γ— 10⁹⁡(96-digit number)
32142952308679767502…15821112736542719999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.214 Γ— 10⁹⁡(96-digit number)
32142952308679767502…15821112736542720001
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
6.428 Γ— 10⁹⁡(96-digit number)
64285904617359535005…31642225473085439999
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 2921880

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 950c75c6a3463a98d7e1da2264c5e7e0347958f59422081aa9a7d69ddd7d136f

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 #2,921,880 on Chainz β†—
Circulating Supply:57,912,763 XPMΒ·at block #6,833,569 Β· updates every 60s
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