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Home/Chain Registry/Block #2,655,609

Block #2,655,609

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/10/2018, 8:03:28 AM Β· Difficulty 11.7041 Β· 4,185,043 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d45b5bc5dd7f0dc14a296e7250c2d53cf45ba944e8a00ddd149e45e95709e705
View on Chainz β†—

Difficulty

11.704055

Transactions

3

Size

1.94 KB

Version

2

Bits

0bb43cf4

Nonce

1,588,901,135

Timestamp

5/10/2018, 8:03:28 AM

Confirmations

4,185,043

Merkle Root

e4ab983d51f0c7d76c9c6747da50f572a68f0bdbe68cdd6677e252c09c1978ac
Transactions (3)
Coinbase9d863739386b90…779b794aef775e
1 in β†’ 1 out7.3100 XPM110 B
AGR5xjhk…Vm5xxfoo
7dc974c26ff01f…ed4246c0e56ac8
5 in β†’ 2 out372.9566 XPM816 B
ASC9um3f…YLq9NmQuAZ11SwEy…s7qssZyS
fc8ca7f739ff16…f5ecd3f4af4e7d
6 in β†’ 2 out345.2831 XPM967 B
AJdM6BQD…g1g59wtyAYpGMJy4…TXxUMxyV
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.

1.975 Γ— 10⁹⁷(98-digit number)
19755111717943419462…19208157716110786560
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
1.975 Γ— 10⁹⁷(98-digit number)
19755111717943419462…19208157716110786559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.975 Γ— 10⁹⁷(98-digit number)
19755111717943419462…19208157716110786561
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
3.951 Γ— 10⁹⁷(98-digit number)
39510223435886838924…38416315432221573119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.951 Γ— 10⁹⁷(98-digit number)
39510223435886838924…38416315432221573121
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
7.902 Γ— 10⁹⁷(98-digit number)
79020446871773677848…76832630864443146239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.902 Γ— 10⁹⁷(98-digit number)
79020446871773677848…76832630864443146241
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
1.580 Γ— 10⁹⁸(99-digit number)
15804089374354735569…53665261728886292479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.580 Γ— 10⁹⁸(99-digit number)
15804089374354735569…53665261728886292481
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
3.160 Γ— 10⁹⁸(99-digit number)
31608178748709471139…07330523457772584959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.160 Γ— 10⁹⁸(99-digit number)
31608178748709471139…07330523457772584961
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
6.321 Γ— 10⁹⁸(99-digit number)
63216357497418942279…14661046915545169919
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 2655609

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 d45b5bc5dd7f0dc14a296e7250c2d53cf45ba944e8a00ddd149e45e95709e705

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 #2,655,609 on Chainz β†—
Circulating Supply:57,969,559 XPMΒ·at block #6,840,651 Β· updates every 60s
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