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Block #3,123,488

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/3/2019, 5:51:27 PM Β· Difficulty 11.3201 Β· 3,718,349 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
269c37f43104013a1ee436961e4cd47a8547082e1dde0c8fde4a3d21f4cf04cd
View on Chainz β†—

Difficulty

11.320135

Transactions

2

Size

2.73 KB

Version

2

Bits

0b51f456

Nonce

578,516,993

Timestamp

4/3/2019, 5:51:27 PM

Confirmations

3,718,349

Merkle Root

e42cfcb6181a6e908daf2e8c79d218141b3c4aa8b4da1a2997800ee58e88421b
Transactions (2)
Coinbased622ffca734b10…a2449e58b366b4
1 in β†’ 1 out8.0300 XPM110 B
AbXwmGxD…4XXYP765
b5c93a54b16a8c…e32c4850152bc2
17 in β†’ 2 out29941.1305 XPM2.53 KB
AQdABV2g…6jsa34vMARQBQiFS…uxviAzfZ
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.

1.631 Γ— 10⁹⁢(97-digit number)
16318260802084608857…92615370439752307200
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
1.631 Γ— 10⁹⁢(97-digit number)
16318260802084608857…92615370439752307199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.631 Γ— 10⁹⁢(97-digit number)
16318260802084608857…92615370439752307201
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
3.263 Γ— 10⁹⁢(97-digit number)
32636521604169217714…85230740879504614399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.263 Γ— 10⁹⁢(97-digit number)
32636521604169217714…85230740879504614401
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
6.527 Γ— 10⁹⁢(97-digit number)
65273043208338435429…70461481759009228799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.527 Γ— 10⁹⁢(97-digit number)
65273043208338435429…70461481759009228801
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
1.305 Γ— 10⁹⁷(98-digit number)
13054608641667687085…40922963518018457599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.305 Γ— 10⁹⁷(98-digit number)
13054608641667687085…40922963518018457601
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
2.610 Γ— 10⁹⁷(98-digit number)
26109217283335374171…81845927036036915199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.610 Γ— 10⁹⁷(98-digit number)
26109217283335374171…81845927036036915201
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
5.221 Γ— 10⁹⁷(98-digit number)
52218434566670748343…63691854072073830399
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 3123488

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 269c37f43104013a1ee436961e4cd47a8547082e1dde0c8fde4a3d21f4cf04cd

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 #3,123,488 on Chainz β†—
Circulating Supply:57,979,070 XPMΒ·at block #6,841,836 Β· updates every 60s
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