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Block #153,626

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2013, 3:30:36 AM Β· Difficulty 9.8631 Β· 6,673,107 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
32952031dc1104642b2663ba700e24b4c918a246340c2fd5dfa818deb614656e
View on Chainz β†—

Height

#153,626

Difficulty

9.863133

Transactions

1

Size

197 B

Version

2

Bits

09dcf647

Nonce

1,406,867

Timestamp

9/7/2013, 3:30:36 AM

Confirmations

6,673,107

Merkle Root

ec48015dd277f42a8ac3dec2b0a67c693a581f532ab2ab983d150902fd896017
Transactions (1)
Coinbaseec48015dd277f4…150902fd896017
1 in β†’ 1 out10.2600 XPM109 B
AKhMrDKq…vFSbv26m
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.

7.389 Γ— 10⁸⁹(90-digit number)
73898884291108133736…71631929869440856000
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
7.389 Γ— 10⁸⁹(90-digit number)
73898884291108133736…71631929869440855999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.389 Γ— 10⁸⁹(90-digit number)
73898884291108133736…71631929869440856001
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
1.477 Γ— 10⁹⁰(91-digit number)
14779776858221626747…43263859738881711999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.477 Γ— 10⁹⁰(91-digit number)
14779776858221626747…43263859738881712001
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
2.955 Γ— 10⁹⁰(91-digit number)
29559553716443253494…86527719477763423999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.955 Γ— 10⁹⁰(91-digit number)
29559553716443253494…86527719477763424001
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
5.911 Γ— 10⁹⁰(91-digit number)
59119107432886506989…73055438955526847999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.911 Γ— 10⁹⁰(91-digit number)
59119107432886506989…73055438955526848001
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
1.182 Γ— 10⁹¹(92-digit number)
11823821486577301397…46110877911053695999
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 153626

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 32952031dc1104642b2663ba700e24b4c918a246340c2fd5dfa818deb614656e

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 #153,626 on Chainz β†—
Circulating Supply:57,858,018 XPMΒ·at block #6,826,732 Β· updates every 60s
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