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Home/Chain Registry/Block #2,653,056

Block #2,653,056

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/8/2018, 2:22:45 AM Β· Difficulty 11.7407 Β· 4,180,019 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
06a977f89b89e2b79f44aa384771f9186e92314edff3271b605fc0c41f13887c
View on Chainz β†—

Difficulty

11.740682

Transactions

1

Size

199 B

Version

2

Bits

0bbd9d51

Nonce

1,173,136,312

Timestamp

5/8/2018, 2:22:45 AM

Confirmations

4,180,019

Merkle Root

81fc51c6372c34967aebf8d3613b9afe321bbcd31b11fd6932e66b5390b09263
Transactions (1)
Coinbase81fc51c6372c34…e66b5390b09263
1 in β†’ 1 out7.2400 XPM109 B
APtxFdXP…qY5hT1eA
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.

1.564 Γ— 10⁹⁴(95-digit number)
15643369185052753412…10617646971719621280
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
1.564 Γ— 10⁹⁴(95-digit number)
15643369185052753412…10617646971719621279
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.564 Γ— 10⁹⁴(95-digit number)
15643369185052753412…10617646971719621281
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
3.128 Γ— 10⁹⁴(95-digit number)
31286738370105506824…21235293943439242559
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.128 Γ— 10⁹⁴(95-digit number)
31286738370105506824…21235293943439242561
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
6.257 Γ— 10⁹⁴(95-digit number)
62573476740211013648…42470587886878485119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.257 Γ— 10⁹⁴(95-digit number)
62573476740211013648…42470587886878485121
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
1.251 Γ— 10⁹⁡(96-digit number)
12514695348042202729…84941175773756970239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.251 Γ— 10⁹⁡(96-digit number)
12514695348042202729…84941175773756970241
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
2.502 Γ— 10⁹⁡(96-digit number)
25029390696084405459…69882351547513940479
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.502 Γ— 10⁹⁡(96-digit number)
25029390696084405459…69882351547513940481
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
5.005 Γ— 10⁹⁡(96-digit number)
50058781392168810918…39764703095027880959
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 2653056

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 06a977f89b89e2b79f44aa384771f9186e92314edff3271b605fc0c41f13887c

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 #2,653,056 on Chainz β†—
Circulating Supply:57,908,773 XPMΒ·at block #6,833,074 Β· updates every 60s
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