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Block #153,591

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/7/2013, 2:53:59 AM Β· Difficulty 9.8631 Β· 6,672,520 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
2f1e7bf9e76b72a1e61c6b360a270087d4644e588c643f707e0484d2812381a7
View on Chainz β†—

Height

#153,591

Difficulty

9.863120

Transactions

1

Size

197 B

Version

2

Bits

09dcf56a

Nonce

98,429

Timestamp

9/7/2013, 2:53:59 AM

Confirmations

6,672,520

Merkle Root

0942f6b48d16a3f9b0b04018f116746e19091f4b2a590933177cfa7590d134be
Transactions (1)
Coinbase0942f6b48d16a3…7cfa7590d134be
1 in β†’ 1 out10.2600 XPM109 B
AM2aZLZw…B8dSVS4x
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.

7.310 Γ— 10⁸⁹(90-digit number)
73106188244841341491…18257707202719029800
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
7.310 Γ— 10⁸⁹(90-digit number)
73106188244841341491…18257707202719029799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.310 Γ— 10⁸⁹(90-digit number)
73106188244841341491…18257707202719029801
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
1.462 Γ— 10⁹⁰(91-digit number)
14621237648968268298…36515414405438059599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.462 Γ— 10⁹⁰(91-digit number)
14621237648968268298…36515414405438059601
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
2.924 Γ— 10⁹⁰(91-digit number)
29242475297936536596…73030828810876119199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.924 Γ— 10⁹⁰(91-digit number)
29242475297936536596…73030828810876119201
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
5.848 Γ— 10⁹⁰(91-digit number)
58484950595873073193…46061657621752238399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.848 Γ— 10⁹⁰(91-digit number)
58484950595873073193…46061657621752238401
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
1.169 Γ— 10⁹¹(92-digit number)
11696990119174614638…92123315243504476799
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 153591

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 2f1e7bf9e76b72a1e61c6b360a270087d4644e588c643f707e0484d2812381a7

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 #153,591 on Chainz β†—
Circulating Supply:57,853,012 XPMΒ·at block #6,826,110 Β· updates every 60s
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