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Home/Chain Registry/Block #1,120,792

Block #1,120,792

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/21/2015, 9:40:51 AM Β· Difficulty 10.9361 Β· 5,679,959 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f1329d02c99ebe0a0c664f7b6f8d03a7cd2c23b37cf468226a0a64c26ecfac96
View on Chainz β†—

Difficulty

10.936137

Transactions

3

Size

2.71 KB

Version

2

Bits

0aefa6a7

Nonce

794,611,127

Timestamp

6/21/2015, 9:40:51 AM

Confirmations

5,679,959

Merkle Root

0283b0a8542ea85d6ffbf1d194f798f069675836429871f2d4c8b95a581cbd52
Transactions (3)
Coinbase7baefd0123d2cc…5759af278ce46f
1 in β†’ 1 out8.3900 XPM110 B
AVyTEpy8…WhY5xB9p
2b6e5befeb09ef…67113b71706971
5 in β†’ 1 out24.0000 XPM715 B
ARezZb4y…FxP7ivbi
bd7b70273c73c9…036b8e064eefe4
12 in β†’ 2 out4.0400 XPM1.82 KB
AGU79Bc8…57oR2nmnAcpj2mhz…D4e86LmU
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.

1.205 Γ— 10⁹⁷(98-digit number)
12054054700706384978…81312722327749836800
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
1.205 Γ— 10⁹⁷(98-digit number)
12054054700706384978…81312722327749836799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.205 Γ— 10⁹⁷(98-digit number)
12054054700706384978…81312722327749836801
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
2.410 Γ— 10⁹⁷(98-digit number)
24108109401412769957…62625444655499673599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.410 Γ— 10⁹⁷(98-digit number)
24108109401412769957…62625444655499673601
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
4.821 Γ— 10⁹⁷(98-digit number)
48216218802825539915…25250889310999347199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.821 Γ— 10⁹⁷(98-digit number)
48216218802825539915…25250889310999347201
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
9.643 Γ— 10⁹⁷(98-digit number)
96432437605651079830…50501778621998694399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.643 Γ— 10⁹⁷(98-digit number)
96432437605651079830…50501778621998694401
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
1.928 Γ— 10⁹⁸(99-digit number)
19286487521130215966…01003557243997388799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.928 Γ— 10⁹⁸(99-digit number)
19286487521130215966…01003557243997388801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10
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 1120792

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 f1329d02c99ebe0a0c664f7b6f8d03a7cd2c23b37cf468226a0a64c26ecfac96

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 #1,120,792 on Chainz β†—
Circulating Supply:57,650,081 XPMΒ·at block #6,800,750 Β· updates every 60s
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