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Block #122,893

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/18/2013, 6:14:56 PM Β· Difficulty 9.7588 Β· 6,704,075 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
af7f4ce45fc7586593b465dc54569fac1f472d5d0e508f2ab6386aed47be04a4
View on Chainz β†—

Height

#122,893

Difficulty

9.758805

Transactions

2

Size

392 B

Version

2

Bits

09c2410b

Nonce

32,899

Timestamp

8/18/2013, 6:14:56 PM

Confirmations

6,704,075

Merkle Root

96ab3357521b640c5ac7332c3ec70978552e44140bfc8e7b26d8c4e55ab0819e
Transactions (2)
Coinbase90c2f0d9f9f7d9…4c60973203017b
1 in β†’ 1 out10.4900 XPM109 B
AYnPP6jG…Q3sS4Pbg
300a8f0bfb49ba…ebbcbae24b0a6a
1 in β†’ 2 out10.4900 XPM192 B
ATu6xjcH…YC1WMrW4AXUtFnVB…2K4kmJnq
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.

5.319 Γ— 10⁹⁢(97-digit number)
53191414760368982236…12673972993690267820
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
5.319 Γ— 10⁹⁢(97-digit number)
53191414760368982236…12673972993690267819
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.319 Γ— 10⁹⁢(97-digit number)
53191414760368982236…12673972993690267821
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
1.063 Γ— 10⁹⁷(98-digit number)
10638282952073796447…25347945987380535639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.063 Γ— 10⁹⁷(98-digit number)
10638282952073796447…25347945987380535641
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
2.127 Γ— 10⁹⁷(98-digit number)
21276565904147592894…50695891974761071279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.127 Γ— 10⁹⁷(98-digit number)
21276565904147592894…50695891974761071281
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
4.255 Γ— 10⁹⁷(98-digit number)
42553131808295185789…01391783949522142559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.255 Γ— 10⁹⁷(98-digit number)
42553131808295185789…01391783949522142561
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
8.510 Γ— 10⁹⁷(98-digit number)
85106263616590371578…02783567899044285119
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9
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 122893

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 af7f4ce45fc7586593b465dc54569fac1f472d5d0e508f2ab6386aed47be04a4

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 #122,893 on Chainz β†—
Circulating Supply:57,859,920 XPMΒ·at block #6,826,967 Β· updates every 60s
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