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Home/Chain Registry/Block #2,655,630

Block #2,655,630

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2018, 8:29:08 AM Β· Difficulty 11.7037 Β· 4,187,505 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d6cef6827a4fd1c10d3222d1bc3a728649c246007e3e686dcd6a26b0c4e1e2a7
View on Chainz β†—

Difficulty

11.703748

Transactions

1

Size

201 B

Version

2

Bits

0bb428db

Nonce

80,653,458

Timestamp

5/10/2018, 8:29:08 AM

Confirmations

4,187,505

Merkle Root

c64a80a8e39136da1964417f7989d47e8e9456ed242957b156d5bbc910a73f3c
Transactions (1)
Coinbasec64a80a8e39136…d5bbc910a73f3c
1 in β†’ 1 out7.2900 XPM110 B
AdjW1FXG…ChXVEQT4
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.

9.259 Γ— 10⁹⁡(96-digit number)
92593301726902186185…44549393818054190080
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
9.259 Γ— 10⁹⁡(96-digit number)
92593301726902186185…44549393818054190079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.259 Γ— 10⁹⁡(96-digit number)
92593301726902186185…44549393818054190081
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
1.851 Γ— 10⁹⁢(97-digit number)
18518660345380437237…89098787636108380159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.851 Γ— 10⁹⁢(97-digit number)
18518660345380437237…89098787636108380161
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
3.703 Γ— 10⁹⁢(97-digit number)
37037320690760874474…78197575272216760319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.703 Γ— 10⁹⁢(97-digit number)
37037320690760874474…78197575272216760321
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
7.407 Γ— 10⁹⁢(97-digit number)
74074641381521748948…56395150544433520639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.407 Γ— 10⁹⁢(97-digit number)
74074641381521748948…56395150544433520641
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
1.481 Γ— 10⁹⁷(98-digit number)
14814928276304349789…12790301088867041279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.481 Γ— 10⁹⁷(98-digit number)
14814928276304349789…12790301088867041281
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
2.962 Γ— 10⁹⁷(98-digit number)
29629856552608699579…25580602177734082559
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 2655630

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 d6cef6827a4fd1c10d3222d1bc3a728649c246007e3e686dcd6a26b0c4e1e2a7

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 #2,655,630 on Chainz β†—
Circulating Supply:57,989,443 XPMΒ·at block #6,843,134 Β· updates every 60s
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